The Tonight Show star was filmed drinking wine at his own wedding and was asked about it by his co-hosts.
Fallon’s appearance on the show this week also drew criticism after he appeared to show his face topless in a video posted on Instagram.
Fallon was filmed at his wedding in February.
The video has since been removed and has been viewed by more than 30 million people.
The clip shows Fallon sitting at a table with two women while wearing a blue tuxedo.
In the background are two men wearing black trousers.
One of the men has his shirt pulled down and is smiling.
He asks if Fallon has a date and asks for his date’s phone number.
Fallon says: ‘I’ve got a date for you.’
He adds: ‘You know what, this is the LAST chance.’
He tells the women: ‘Get ready for a date with me.
I want to have a real relationship with you.
I’m gonna have a date tonight.’
The men in the video say they will be ‘getting ready’ to go on a date.
‘The show is going to go out, and I want you to be on it,’ Fallon says.
‘You gotta go out and meet people, you gotta go make people laugh.’
The video, which has now been removed from Instagram, has been shared more than 2.4 million times.
The star has previously been criticised for appearing to take pictures of himself without permission.
Fallon tweeted a photo of himself with his hands on his knees and said: ‘There are some things that should be private.’
His wife Victoria Beckham posted a photo to Instagram of herself in a dress with a caption: ‘When I’m not wearing clothes, I’m feeling so sexy and sexy and beautiful.
It’s just that one thing I know that I want everyone to know.’