Fernando Morena Pena, who governed between 1997 and 2003, was with the former dean of the University of Colima when two people entered the restaurant and opened fire, a spokesman for the state public security department told AFP.
The spokesman said Morena Pena, a member of the ruling Institutional Revolutionary Party (PRI), was taken to a hospital where he underwent surgery.
Late Monday, cardiovascular surgeon Emanuel Martin del Campo at the regional university hospital said Morena Pena was now "out of danger."
PRI president Manlio Fabio Beltrones urged authorities to find those responsible for the attack and "punish them to the full extent of the law."
"I regret and deplore" the assault, he added.
Another former Colima governor, Silverio Cavazos, was shot dead outside his house in 2010.
