The force didn’t reveal which officials the pair are accused of targeting, citing an ongoing investigation.
Officers said the two suspects, a 32-year-old funeral director and a 61-year-old retiree, were arrested in Ma On Shan and Lamma on Wednesday.
Chief Inspector Tai Tze-bun from the Cyber Security and Technology Crime Bureau said the older man is also suspected of encouraging others to spread the coronavirus.
Tai said if people had acted on the alleged calls for violence, it would have led to serious disruption to public order.
He added that more arrests could be made.
Police said they seized three mobile phones, a laptop, and another mobile device as part of the investigation.