Irishman Martin placed third in last year's edition, and was seeking another podium spot for his new squad, UAE Team Emirates, this year.
However, the 31-year-old appeared to be struggling during Saturday's climb-filled stage from Nice to Valdeblore La Colmiane and called it a day after around 85km of the 175km route.
Martin was among a number of riders to call it quits during the stage, with UAE team-mate Alexander Kristoff also climbing off.
Mike Teunissen (Team Sunweb), Julien El Fares (Delko Marseille Provence), Koen De Kort (Trek-Segafredo) and Bert Van Lerberghe (Cofidis) were among the abandons. French sprinter Arnaud Démare (Groupama-FDJ) was a non-starter, citing poor weather.
At the start of the day, the race's organiser reported that only six of the 22 teams still had their full complement of seven riders in the race. LottoNL-Jumbo had started the day with only three riders.
Team Sky lost Wout Poels after he crashed during Friday's stage and abandoned after fracturing his collarbone. He had been in second place overall behind leader Luis Leon Sanchez (Astana), and Sky is now rallying behind 2017 Paris-Nice winner Sergio Henao.
With the cold, wet conditions set to continue and with the possibility of snow on the final climb to Valdeblore La Colmiane, more abandons are expected.
Paris-Nice concludes on Sunday.
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