Jennings tweeted: "Headed home to rest up with my family. Thanks again everyone for the kind words."
The Marlins on Friday placed Jennings on the seven-day concussion disabled list. But that doesn't mean he automatically will return in a week. If he needs more time, he can be transferred to the 15-day DL.
Jennings received a scare in the seventh inning of the Marlins' 7-2 loss to the Pirates on Thursday. Jordy Mercer's comeback liner deflected off the left side of the reliever's head.
Jennings also expressed his thanks to Mercer for his concern.
Via Twitter, the reliever wrote: "Also thanks to @jordy_mercer for reaching out, class act."
A CT scan taken Thursday night came back negative.
"Everything checked out fine," Miami manager Mike Redmond said. "It's good news he was cleared to fly back home. It tells a lot about how he's doing. He will get home and rest. We will monitor and know more when we get back to Miami.
"We definitely feel that he made it through a scary situation. It looks like he will be fine and make that full recovery."
Joe Frisaro is a reporter for MLB.com. He writes a blog, called The Fish Pond. Follow him on Twitter