Rihanna's IV Picture -- Flu Da One

There's a reason Rihanna's arm was hooked up to a bunch of needles and tubes yesterday -- sources close to Rihanna tell TMZ, the singer had been struck down with a bad case of the flu ... and required an IV drip.

Sources tell us, she started feeling really ill last week and saw a doctor on Thursday ... but by the time of her "Saturday Night Live" appearance, she still wasn't fully recovered.

As we first reported, Rihanna missed the SNL dress rehearsal because she was sick -- but show producers didn't buy her excuse ... insisting she didn't appear ill.

But looks might be deceiving -- because we're told Rihanna wasn't just ill during her SNL performance, she also continued to feel sick the next few days ... and her doc was forced to put her on Penicillin.

Soon after, Rihanna began to experience flu-like symptoms -- requiring IV treatment yesterday, which is when she posted the above picture on Twitter.