The former Osbournes star was recently reported to have married longtime girlfriend Lisa Stelly in a private ceremony on the island on Sunday (October 7).
Osbourne was relaxing on the beach with a friend when the incident occured, WENN reports.
He spotted a woman near the coast of the island, suffering from a heart attack. Osbourne swam out to her, pulling her to shore.
Stelly told readers of her Twitter page: "Really proud of Jack and his friend Tyler who saved a woman on the beach yesterday who'd had a heart attack and drown (sic).
"They resuscitated her until the ambulance came. We just found out she's in a stable condition! Awesome!"
Osbourne recently confirmed that he has been diagnosed with multiple sclerosis.