Ozzy Osbourne's Former Guitarist Jake E. Lee Shot in Las Vegas Walking His Dog

1:31 PM PT -- Ozzy Osbourne tells TMZ ... “It’s been 37 years since I’ve seen Jake E. Lee, but that still doesn’t take away from the shock of hearing what happened to him today. It’s just another senseless act of gun violence. I send my thoughts to him and his beautiful daughter, Jade. I just hope he’ll be ok.”

Jake E. Lee, best known for being Ozzy Osbourne's guitarist, has been hospitalized following a shooting in Las Vegas ... TMZ has learned.

The musician's rep tells TMZ ... Jake was shot multiple times early Tuesday morning while taking his dog out for a walk in Las Vegas, Nevada.

Jake is now fully conscious and doing well after the attack ... though, he's currently in an intensive care unit in a hospital in Vegas. He is expected to make a full recovery.

Authorities investigating the case do not currently believe Jake was targeted in the bout of violence ... as they believe the incident around 2:40 AM was a "completely random" street shooting. Police are investigating the incident. No arrests have been made, according to Las Vegas Metro Police.

Jake and his family ask for privacy as the guitarist recovers from his injuries.

As you might recall, Jake took over as Ozzy’s lead guitarist in '82 after Randy Rhoads’ tragic death, and he left his mark on classic albums like '83’s "Bark at the Moon" and '86’s "The Ultimate Sin."

He’s also known for shredding some killer solos on tracks like "Shot in the Dark" and "Killer of Giants."