Tony Choi was earlier found guilty of incitement to cause grievous bodily harm.
The court heard he posted the message a day after a protest in Central in January last year in which a number of officers were injured.
In mitigation, his lawyer said the defendant has no chance of committing the offence again because he intends to leave Hong Kong.
Choi’s sister, who’s in the US, also wrote to the court that her brother broke the law on impulse, saying he’s a generous person.
In sentencing, judge Clement Lee said social media can spread messages rapidly and described the defendant’s message as “an intentional expression that was irrational and inciteful”.
The judge reduced the jail term by a month, saying the defendant’s unlikely to commit the same offence, he’s not a famous person and his message received fewer than 100 responses.
The police’s Cyber Security and Technology Crime Bureau welcomed Choi’s sentencing, saying it would act as a deterrent.