The replay showed the ball bounced off the back of West's head as he faced home plate. West called timeout and huddled with the rest of the crew and a member of the Miller Park security team.
West appeared to be fine and walked back to his base, with play resuming shortly thereafter.
Marlins pitcher Brad Ziegler, who is on the disabled list with a back strain, tweeted: "I hope they file assault charges for whoever just hit Joe West with the baseball. Absolutely ridiculous.''
The 64-year-old West, nicknamed "Cowboy'' Joe, worked his 5,000th career regular-season game last week. He's the third umpire to work at least 5,000 games, joining Hall of Famer Bill Klem (5,375) and Bruce Froemming (5,163).
West made his major league debut as a 23-year-old on Sept. 14, 1976. He joined the National League staff full time in 1978. His 40 seasons umpiring in the majors are the most by any umpire.
West also has also worked two All-Star Games, 123 postseason games and six World Series.
The Associated Press contributed to this report.