Mr Kwon was found guilty of forging official documents.
He was arrested in March as he tried to board a flight to Dubai at Podgorica Airport, in the country’s capital.
Mr Kwon also faces charges in the US and South Korea over the collapse of the two digital tokens last year.
The former finance officer of Mr Kwon’s company Terraform Labs, Han Chang-joon, was also sentenced to four months in prison after being found guilty of the same charges.
Mr Kwon and Mr Han pleaded not guilty at their first court hearing in May.
The sentences will include the time that Mr Kwon and Mr Han have already spent in detention after being arrested in March, the court said in a statement.
They will also be able to appeal the verdict within eight days of receiving written notification from the court.
In February, US regulators charged Mr Kwon and his company Terraform Labs with “orchestrating a multi-billion dollar crypto asset securities fraud”.
“We allege that Terraform and Do Kwon failed to provide the public with full, fair, and truthful disclosure as required for a host of crypto asset securities, most notably for Luna and TerraUSD,” US Securities and Exchange Commission (SEC) chairman Gary Gensler said in a statement.
Last year, a South Korean court issued arrest warrants for Mr Kwon and five other individuals connected to the case.
Prosecutors said they believed that Terraform Labs, which is registered in Singapore, had violated capital market rules.
Montenegro does not have extradition treaties with the US or South Korea.
The collapse of the terraUSD stablecoin and the associated Luna token rocked cryptocurrency markets in May 2022.