Rihanna faces legal troubles!

According to legal docs filed Thursday in New York -- and obtained by TMZ -- a Brazilian promotion company called Unique Sports and Marketing signed a $1.7 million agreement to book Rihanna for three Brazil shows in November.

Problem is -- Unique claims the people who said they signed the contract on Rihanna's behalf -- a company called Vegas Style Entertainment -- never repped Rihanna ... never ever.

Unique claims Vegas Style hatched a fraudulent con scheme  -- and by the time the Brazilians figured it out  ... they had already forked over $825,000.

Unique wants $4,685,000.  Calls to Vegas Style were not returned.