The rapper got thrown in cuffs and hauled off to jail early Saturday morning at Newark Liberty International Airport -- where cops say she and some people she was with got into a fight with another group ... something TMZ Hip Hop now has on surveillance footage.

Check out the video ... you can see a few dudes catapult into frame at one of the terminals, immediately falling to the ground and going at it with fists, before Sexyy enters the frame.

She's the one wearing the red bonnet, and from the looks of the video ... she too was very much ready to throw down. Rather than jump into the dogpile, though, she ended up using a stand on the ground and waving it around as if she's ready to use it on someone.

It doesn't appear Sexyy made any contact with anyone here -- luckily someone else jumped in and pulled her away from all the madness -- but she was right in the mix for a bit there.

Airport personnel/security can also be seen running trying to wrangle everyone -- there's a lot of shuffling going on, and SR and co. can be seen going in and out of a door there at the terminal too. Eventually, cops showed up and arrested a few individuals ... Sexyy included.

Still unclear what exactly led up to this bruhaha -- but the Port Authority tells TMZ ... Sexyy was ultimately arrested for disorderly conduct -- while a couple others in the fight got booked on assault charges. As for the alleged victims ... we're told they went to the hospital for minor injuries.

Sexyy herself already appears to have addressed this -- she hopped on social media later this weekend, saying she "just got out" ... and later offering to replace the phone of the people she got into an "altercation" with at the airport. So, she seems to have a good attitude about it.