The Timberwolves center went out to celebrate his cake day after his game against the Suns on Monday ... but was not aware that a surprise bash was waiting for him.

You can see the 6'11" All-Star and Woods walk into what appears to be a restaurant, when a big crowd screamed "SURPRISE" -- and KAT was in complete shock!!

The fun didn't stop there ... KAT, Woods, friends and fam took the party back home as you can see Towns in his PJs and flops enjoying his birthday cake.

Then it was gift opening time -- Woods hooked her man up with a leather Louis Vuitton Alzer 80 bag ... which comes with a removable interior tray, lock with key and protective cover.

This bag comes with a $13,000 price tag before the custom artwork Woods had done on it ... which features "4:13" on one side and "KAT" on the other.

BTW, 4:13 is a bible verse, "I Can Do All Things Through Christ Who Strengthens Me." It also has the date Towns' mother, Jackie, died from COVID (April 13, 2020).

There seems to be a bit of a trend -- Woods also got him an LV bag featuring his mother's name with a halo and angel wings for his birthday last year.