In the picture, she wore a long-sleeve shirt and smoked a cigarette, reported Us magazine.
"They invented #fbf for moments like this," Paltrow, 42, wrote.
Paltrow and Leitch dated in the early '90s, before she went on to romance stars such as Brad Pitt, Ben Affleck, and now estranged husband Chris Martin.
In March 2014, just months before calling it quits with the Coldplay rocker, Paltrow was spotted kissing Leitch during an LA Dodgers game.