Federer, who withdrew last week from Madrid with back pain, admitted on Wednesday he had been surprised to get past second round opponent Alexander Zverev in straight sets.
Rome marks only the fourth tournament of the season for Federer, who underwent knee surgery in early February, the first operation of his career.
The 17-time Grand Slam champion only decided to face Thiem at the last minute on Central Court, and the Austrian capitalised to finish off an obviously ailing Federer in 1hr 18mins.
In the quarterfinals, Thiem will now play either French 11th seed Richard Gasquet or Japan's sixth seed Kei Nishikori, who face off in a third round clash later on Thursday.
Federer admitted he was happy to exit the tournament, which he has never won, because it will give him time to consider his options as he tries to regain full fitness ahead of next month's French Open at Roland Garros.
He said he will now consult his team about whether to remain in Italy, travel to France or return home to Switzerland.
But as for competing in Rome, Federer said: “My body's just not ready… I'm not going to go into specifics, because I'm not in the mood.
“Ten days before (the) Monaco (tournament), I trained really well on clay and I thought it would give me a good chance in Paris.”
His second round win on Wednesday was the first for the 34-year-old Swiss since losing a Monte Carlo quarterfinal to Jo-Wilfried Tsonga nearly a month ago.
Federer said his outlook has all changed in the “last couple of weeks” and added: “The way I'm playing right now is not going to be good enough for a good run in Paris.
“It really depends now on the next seven to nine days, how I can really play in Paris. I'm going to have a meeting with my team, talk about options we have, stay in Rome, Paris or go back to Switzerland.
“Should I rest, train, do some more physio ? All that stuff needs to be discussed but I'm so happy I didn't get hurt this week.
“Happy I'm through the tournament now and can look ahead. I can pace myself. In a match you can't really pace yourself.”
Meanwhile, it could be the beginning of a Rome Masters fairytale for 22-year-old Austrian Thiem, who is approaching 30 wins for the season having secured two titles already and suffered defeat to Germany's Philipp Kohlschreiber in the final at Munich nearly a fortnight ago.
Later, defending champion Novak Djokovic faces Brazilian Thomaz Bellucci while seven-time winner Rafael Nadal plays Australian Nick Kyrgios.
TENNIS
Austrian triumphs over ailing Federer in Rome
Swiss third seed Roger Federer's Rome Masters bid ended with a 7-6 (7/2), 6-4 third round defeat to Austrian 13th seed Dominic Thiem on Thursday.
ROGER FEDERER
Is this the end of the road for Swiss tennis legend Roger Federer?
Roger Federer is talking optimistically about returning to his "highest level" after knee surgery, but does tennis have to start adjusting to a future without the Swiss star?
The 20-time Grand Slam winner announced on Wednesday that he would be sidelined until 2021 after his second operation in a matter of months.
Federer remains upbeat, tweeting: “I plan to take the necessary time to be 100 percent ready to play at my highest level.”
In some ways 2020 is a good season to miss after the coronavirus ravaged the tennis schedule. Writing Federer off in the past has proved dangerous.
He returned from a six-month injury lay-off to claim the Australian Open in 2017, winning his eighth Wimbledon crown later that year.
But he will be 40 in 2021 and is now heading into uncharted territory.
Despite his groaning trophy cabinet, there are two factors that will motivate Federer to keep going — the risk of losing his grip on the men's Grand Slam title record and a missing Olympics singles gold medal.
Rafael Nadal has 19 majors, just one shy of Federer's mark and Djokovic has 17.
Spain's Nadal will be fancied to draw level with Federer at the French Open, rescheduled for September, while few would bet against Djokovic winning in New York weeks earlier.
In April, Federer said he was “devastated” when Wimbledon was cancelled for the first time since World War II. Last year he fell agonisingly short at the All England Club, failing to convert two championship points on his own serve against Djokovic.
The Wimbledon grass probably remains his best chance of adding to his Grand Slam collection — he has not won the US Open since 2008 and his only title at Roland Garros came in 2009.
Even though Federer has slipped from the very pinnacle of the game, he is still a major threat to Nadal and Djokovic.
'Golden' ambitions
Last year, the world number four had a 53-10 win-loss record and he reached the semi-finals at the Australian Open in January in his only tournament this year.
Federer, who is still six ATP titles short of Jimmy Connors' all-time record of 109, has one glaring omission from his CV — the Olympic title.
The Swiss won doubles gold in Beijing in 2008 with compatriot Stan Wawrinka but lost in the singles final to Andy Murray in London four years later.
The postponed Tokyo Games will almost certainly be Federer's last opportunity to complete a career “golden” Grand Slam — he will turn 40 on the day of the closing ceremony next year.
Tennis will feel the loss of the elegant Federer keenly when he walks off the court for the last time.
Djokovic and Nadal have been the dominant forces in recent years but the Swiss remains the biggest draw and last month topped Forbes' list of the world's highest-earning athletes.
His last appearance on court was in front of nearly 52,000 fans — touted by organisers as a world record for tennis — at a charity match against Nadal in Cape Town in February.
Federer is nearly always the crowd favourite wherever he plays and has proved a perfect ambassador for the sport since he won his first Grand Slam title in 2003.
He certainly expects to be back and competitive next year.
“I will be missing my fans and the tour dearly but I will look forward to seeing everyone back on tour at the start of the 2021 season,” he tweeted.
The avalanche of support from his adoring fans showed they would miss him too, but they will have to get used to a time when he is gone for good.
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