Minter and a pilot were in a single-engine Cessna when it crashed just after 3 p.m. in front of beachgoers near the busy Santa Monica Pier.
Police say the pilot, who has not been identified, suffered minor to moderate injuries but is expected to be OK.
According to the Federal Aviation Administration, the pilot made an emergency landing after reporting engine issues. The agency said the plane had just departed from Santa Monica Airport.
AIR7 HD was above the scene as crews worked to move the Cessna from the shore. Video obtained by Eyewitness News shows the moment the aircraft slammed into the waves and flipped over onto the sand.
Small plane crashes, flips over on Santa Monica beach
Current Santa Monica Mayor Gleam Davis confirmed Minter's death on social media Thursday night.
"The City is grateful for Mr. Minter's public service and we join his family in mourning his passing," said a statement from the city. "Flags in front of City Hall will be lowered to half-staff and a City Council meeting in the new year will be adjourned in honor of Minter's service."
Flags at Santa Monica City Hall lowered for Rex Minter, former mayor who died in plane crash
Minter was born in 1927, elected to the Santa Monica City Council in 1955 and was mayor from 1963 to 1967.
He also served as city attorney for Arcadia and as a judge for the Los Angeles County Superior Court.
Flags in front of Santa Monica City Hall on Friday were lowered to half-staff to honor Minter.
The National Transportation Safety Board is investigating the cause of the crash.
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