Mary J. Blige -- Broke Bikini Babe!

Mary J. Blige isn't letting a little thing like financial ruin stop her from vacationing in the Caribbean.

Rockin' a sexy green bikini, the 42-year-old cash-strapped R&B diva tried to get her mind off the $900K tax lien she got hit with in February ... and defaulting on a $2 million bank loan last year ... and the $250K bank loan her charity was sued for ... by somehow finding the means to jet down to Puerto not-so Rico this weekend.

All that drama has Mary feeling the heat.

2:35 PM PT -- A rep for Mary tells us the singer, "was performing at an event, she was NOT vacationing."