He's since recovered and is trying to help others by donating plasma.
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Palka visited the Red Cross donation center in Woodland Hills recently to answer the call to serve in a different way.
"I became ill in mid-March in the first wave of Los Angeles police officers," he recalled. "Had all the symptoms - fatigue, fever, shortness of breath. Massive fatigue hit me hard."
The 56-year-old is now a COVID-19 survivor whose plasma, like that of others who have recovered from the disease, is now in demand.
It's still considered an experimental treatment, but convalescent plasma - rich with antibodies that can fight the coronavirus - is taken from a recovered person and given to a sick patient to help them fight off the virus.
"It's been used in the past for things like influenza in 1918," said Dr. Ross Herron, American Red Cross divisional chief medical officer. "We tried it for Ebola so now it's a chance to maybe fight off COVID-19."
Palka is no stranger to the Red Cross. He says his father had a rare blood type - O-negative - and would regularly donate blood.
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"He had taught me the importance of giving back and his way of serving and helping others was to donate his own blood," Palka said. "And I've never forgot that message."
Police Chief Michel Moore says Palka is among 110 LAPD personnel to test positive for COVID-19. He says just over 50 have recovered and are back on duty.
"After surviving this virus, it doesn't surprise at all that he steps into this role and models what we hope other COVID-19 survivors do," Moore said.
If you're a coronavirus survivor and you wish to donate your plasma you can get information from the Red Cross here.
Donating plasma takes about an hour. The Red Cross says convalescent plasma donors then have to wait 28 days before providing another donation. Palka says he expects to be back next month to help out again.