The Argentina defender last featured in United's 1-1 draw with West Ham in February. He then missed five consecutive games, starting with the win at Everton, due to the injury.
Michael Carrick's squad are in the Republic of Ireland's capital for an intensive four-day training camp, preparing for the final seven games of the Premier League season, with a place in next season's Champions League at stake.
Martinez was a welcome sight on Monday, joining the squad after months away from first-team action. The 28-year-old trained fully in front of club cameras as he works on regaining match fitness.
United will return to Premier League action next Monday when Leeds United visit Old Trafford. This will be the first game after a 24-day break, which included the March international fixtures and the Emirates FA Cup quarter-finals.
Carrick is expected to provide further squad updates throughout the week as United push towards a strong finish to the season.