Ultra Concert Goers -- Meet and Greet With DJs ... in the ER

A crapload of EDM fans got up close and personal with Avicii during the Ultra Music Festival Saturday night in Miami ... but no backstage ... in the hospital.

Law enforcement sources tell TMZ ... 51 people were treated at Ultra for medical emergencies last night -- including possible overdoses and "dancing injuries."

We're told 15 required hospitalization.

No word on whether they actually got to meet Avicii -- who's also in the hospital and penciled in today for gall bladder surgery.