Experts say the threat could be an attempt to press Rainsy into ending the opposition's boycott of parliament called after last year's election.
The poll returned Hun Sen to power but is hotly disputed due to allegations of massive vote-rigging.
Hun Sen said Rainsy insulted King Norodom Sihamoni in the letter last week - appearing to take issue with the monarch for congratulating parliament on convening despite months of protests against the poll result.
Under Cambodian law anyone who disrespects the council, the nation's top legal body, can face punishment - including jail - although nobody is believed to have been imprisoned for the offence so far.
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Local media reports said Rainsy could face up to a year in jail if found guilty.
"For the case of insulting the king, there is no law to hand out a punishment... But don't forget by opposing the Constitutional Council you (Rainsy) are guilty," Hun Sen said in a televised speech.
"The government is thoroughly considering this issue," he said, adding that Rainsy already faces charges of inciting garment workers to strike.
That incident in January ended in a bloody crackdown by authorities that left four factory employees dead.
The premier said backroom talks with the opposition over their differences were continuing, in a sign he may use mounting legal challenges as a bargaining chip with Rainsy.
During a ceremony to mark the first anniversary of the formation of his opposition Cambodia National Rescue Party, Rainsy played down the legal threats against him.