The musician apparently took to the social network to complain about Mayer after reading a profile in Rolling Stone.
"I love how the 'neil young of our generation' self-naming king douche grows his hair out + buys a place in Montana just to do RS article," he wrote.
Jennings continued: "Claims he's 'done w hollywood game' and has 'roots' and then immediately cuts hair, goes back to hollywood clubs + starts banging Katy Perry."
Jennings also attacked Mayer's skills as a musician, saying: "And don't anybody say he's a great guitar player. Gary Clark Jr & @lukasnelson wipes their asses with this dude."
"That's enough, John Mayer," he later said, before apparently apologising for his tweets, writing: "Sorry to s**t talk. Lord knows not everybody likes my ass. But seeing that RS in my friggin bathroom & reading the narcissistic drivel..."
Jennings went on to retweet several messages which criticised his remarks and accused him of being jealous of Mayer.