MEXICO CITY (Reuters) - SurveyMonkey chief executive Dave Goldberg died Friday from a head injury while exercising at a resort in Mexico, the local prosecutor's office said Monday.

Goldberg, the husband of Facebook Inc chief operating officer Sheryl Sandberg, fell off a treadmill at a private villa in Punta Mita and hit his head, the prosecutor's spokesman said.

Goldberg's brother found him on the floor of the villa gym showing signs of life, the spokesman said. He was taken to the hospital, where he later died.

No criminal investigation is planned as there were no signs of violence, the spokesman said.

He said the accident happened at the Palmasola at the Four Seasons Resort, a private 9-bedroom beach front villa, which gives guests access to the facilities of the Four Seasons. Punta Mita is located near the Mexican west coast vacation town of Puerto Vallarta.

Goldberg's brother announced his death on Saturday morning via a Facebook post, and SurveyMonkey also put out a short statement.

One of Silicon Valley's most admired entrepreneurs, Goldberg was known for his low-key demeanor and the grace and good humor with which he handled being married to one of the nation's most recognizable executives.

Under his leadership, privately held poll-taking company SurveyMonkey grew into a US$2 billion business.

A memorial service for Goldberg will be held on Tuesday at Stanford University, according to friends of the family.