Jemima Kirke: Kicked Out of Jay-Z "Picasso Baby" Shoot For Clinging to Rapper?

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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."

Even though Beyonce's spouse kept his cool and didn't skip a beat, his security team saw Jemima Kirke going bananas and peeled her off the rap icon.

“Someone was screaming ‘Get her off of him!’” says a spy. Kirke went away kicking and begging, “Let us finish!” as she was removed from the gallery.

Called for comment about her alleged meltdown, Kirke reps said they knew nothing of it, while the video's director called this "complete bull$h!t" ... so who knows.

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