Health scare for Liev Schreiber … he’s hospitalized in New York City, where he’s going through a battery of tests.

Sources with direct knowledge tell TMZ … the “Ray Donovan” star had a massive headache Sunday and he called his doctor, who told him to immediately go to a hospital.

We’re told Liev followed his doctor’s advice and stayed overnight Sunday at a NYC hospital … and today, doctors have been running tests on him.

It’s unclear what is ailing Liev — our sources say doctors don’t know the nature of the problem — but we’re told Liev is able to speak and walk without any issues and has the full use of his limbs.