Los Angeles announced the move Saturday before a game against the Colorado Rockies.
The injury-plagued Dodgers currently are without starters Clayton Kershaw (back), Rich Hill (blisters) and Kenta Maeda (hip). Another starter, left-hander Hyun-Jim Ryu, was transferred to the 60-day disabled list on Saturday. He originally was placed on the DL with a strained groin on May 3.
The 24-year-old Conlon made his major league debut on May 7. He appeared in two games with the Mets and had an 11.12 ERA.
Conlon, who is from Belfast, Northern Ireland, was selected by the Mets in the 13th round of the 2015 draft out of the University of San Diego.