LOS ANGELES (Reuters) - Former California Governor Arnold Schwarzenegger said on Monday that his 13-year-old son, Christopher, is improving as he recovers from injuries suffered when he was hit by a large wave at the beach.

"Thanks for all your support for Christopher," Schwarzenegger wrote in a Twitter post. "It means a lot to me & to him. He's doing much better & we'll have him back at full speed soon."

The celebrity news website TMZ.com has reported the youth was severely injured when he was hit by a large wave while surfing or boogie-boarding last weekend in Malibu, suffering multiple broken bones and a collapsed lung.

Schwarzenegger and his estranged wife, Maria Shriver, issued a joint statement last week saying only that their son, the youngest of their four children, had been hurt in a beach accident but was expected to make a full recovery.

Shriver filed for divorce from Schwarzenegger on July 1, weeks after the Austrian-born former bodybuilder and film star publicly admitted to fathering a child out of wedlock with a member of the family's household staff over a decade ago.

(Reporting by Alex Dobuzinskis: Editing by Steve Gorman and Cynthia Johnston)