A 3-month-old baby is clinging to life after he was found unconscious inside a Lower East Side apartment this week — and investigators believe the baby had been shaken, according to police sources.

The infant was discovered inside the Water Street apartment, on the grounds of NYCHA’s Vladeck Houses, around 8:10 p.m. Monday, cops said.

There were no visible signs of trauma, but the infant is believed to be a victim of shaken baby syndrome.

The tot was taken to NewYork-Presbyterian Weill Cornell Medical Center, where he was still listed in critical condition Wednesday morning.

The boyfriend of the child’s mom had been babysitting him that day, police sources said.

Cops could not immediately confirm whether he was in custody Wednesday.