Molina has been out since July 8 with a right-thumb tendon stain and missed 28 games. He was out 12 games earlier in the season with a similar injury and had initially been expected to miss about three weeks this time.
A nine-time All-Star, Molina is hitting .261 with four home runs and 36 RBIs in 71 games this season.
Martinez left Sunday's game against the Pittsburgh Pirates in the fifth inning with right-shoulder discomfort. He is hitting .266 with 10 home runs and 40 RBIs in 2019.
The Associated Press contributed to this report.