by Free Britney at . Comments

Jay-Z allegedly had back problems while filming a 10-minute performance video for "Picasso Baby" this week ... because Jemima Kirke was hanging on it.

According to sources at midtown’s Pace Gallery, he needed help from security to lighten the load as the Girls actress "clung to him like a cheap suit."

The shoot began innocently enough, with Hova serenading her, and the smiley actress keeping it together as she let down her hair and grinned away.

A short time later, the video cut to Kirke ALL over Jay as he rapped to the crowd.

“She was acting totally nuts!” said a witness who watched Kirke climb onto Jay’s back and hold on tightly as the hip-hop superstar "walked about."

“She kept jumping on his back like a little monkey."

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