Mandel's decision -- announced in an email to supporters Friday -- means Republicans have suddenly lost their leading candidate in a state President Donald Trump won by 9 percentage points in 2016.
The GOP controls the Senate 51-49, and although more Democrats are at risk than Republicans this year, Trump's national unpopularity means Democrats have a chance of taking control.
"We recently learned that my wife has a health issue that will require my time, attention and presence. In other words, I need to be there," Mandel, the Ohio state treasurer, said in the email.
"Understanding and dealing with this health issue is more important to me than any political campaign. For as long as that takes, whether it is months or years, it is important that I heed my dad's advice and be there for my wife and our kids," Mandel wrote. "After recent discussions with our family and healthcare professionals, it has become clear to us that it's no longer possible for me to be away from home and on the campaign trail for the time needed to run a US Senate race."
Who will be the GOP nominee?
Republicans currently running for governor -- Rep. Jim Renacci, Lt. Gov. Mary Taylor and former Sen. Mike DeWine -- could also re-evaluate their options with Mandel out of the race. A Taylor aide said she is receiving calls gauging her interest in a Senate run.
The retiring Rep. Pat Tiberi was the first possible candidate on many Republicans' minds. He already has $6.6 million in the bank, according to campaign finance records -- enough to jump-start a statewide campaign.
But in 2017 Tiberi passed on a Senate run, citing family obligations. And a spokesman told the Cincinnati Enquirer that Tiberi won't change his mind.
"The congressman's decision in May to not pursue a Senate run had nothing to do with Josh Mandel and the congressman looks forward to starting his new role with the Ohio Business Roundtable on January 16," Tiberi spokesman Rob Nichols told the newspaper
Rep. Dave Joyce and venture capitalist J.D. Vance, known for his book "Hillbilly Elegy," are other potential candidates being mentioned by Republican strategists.
Ohio Gov. John Kasich, a fierce Republican critic of Trump in his last year in office, will not run for the Senate seat, adviser John Weaver said.
The field will shape up quickly: Ohio's filing deadline for the Senate race is February 7. Michael Gibbons, a Cleveland-area banker and major Republican donor, is the only other GOP candidate in the race.
Mandel was running for the second time against Brown. He lost a competitive race in 2012.