A Staten Island cop wounded in a fatal shootout with a career criminal left the hospital to a hero’s reception Wednesday — but will need months of rehab before she can return to work.

Police Officer Vanesa Medina, 30, was struck in the left hand Tuesday during a shootout with a domestic violence suspect who was shot dead by police after squeezing off two rounds at cops.

Doctors said the four-year NYPD veteran, who is right-handed, will have her left arm in a sling for up to five weeks, then will require up to six months of recovery time and physical therapy before she can don the uniform anew.

“I think she’ll get 80-90, even 100 percent of her hand functions back over the next 3-6 months,” said Dr. Biagio Pacifico, the surgeon who operated on the cop. “She was happy she didn’t lose her hand in general.”

Medina was shot around 8:45 a.m. Tuesday on Prince Street in Clifton, when she and another officer approached suspect Gregory Edwards, 39.

Edwards, who had 16 arrests on his criminal record, tried to flee and struggled with the officers, who zapped him with Taser — but the jolt failed to stop him and he got off two shots with a Sig-Sauer handgun, police said.

Police said Medina’s partner, Raychel Campanella-Rivera, who joined the force in 2014, was the cop who deployed the Taser, and then opened fire and struck Edwards.

Medina is seen on video in the aftermath of the shooting clutching her bloodied left hand as other officers rush her to a police vehicle, which drove her to Richmond University Medical Center.

On Wednesday, dozens of officers lined up outside the hospital around 1 p.m. to applaud her as she was wheeled out of the main entrance — then stood up and walked to a waiting vehicle.

“Every New York City police officer knows it could have been them and that’s why we came out here for our sister,” Police Benevolent Association union President Pat Lynch said.

“When that perp raised the gun and pulled the trigger, we deescalated the situation,” Lynch said. “We shot him to make him stop from hurting anyone else. He tried to kill a New York City police officer, he would have tried to kill anyone else across the street.”

Meanwhile, a memorial for Edwards sprung up at the site of the shootout — where onlookers Tuesday pelted police with profanities and yelled death threats after Edwards was killed.