The "Uncut Gems" actor appeared virtually on the U.S. late night talk show host's programme, amid the Covid-19 lockdown, to help remind viewers to keep their distance from the elderly during the pandemic.
Fallon, 45, and Sandler, 53, both strummed along to guitars as they provided vocals for the tune.
"I love my grandma so much / I know she loves me, too," Fallon sang, as Sandler added, "But thanks to this stupid virus / There are some new grandma rules."
In unison, they crooned, "Don't touch grandma / leave her alone / you can spend a quarter to call her on the phone. So don't touch grandma / Keep it to Zoom / Or learn to play canasta from across the room."
Sandler then urged listeners to tell their grandma, "no touchy, just looky," adding, "Don't touch grandma / give her some space / even if your grandma wants to go to second base."
The pair then concluded by reminding fans that, "you still can smell her grandma smell from six feet away."
The new song comes after Sandler recently performed a number dubbed "The Quarantine Song" on Fallon's online version of "The Tonight Show", which applauded healthcare workers for their efforts in fighting the coronavirus.
"Don't Touch Grandma" is available to watch on the official "The Tonight Show Starring Jimmy Fallon" YouTube channel.