The 33-year-old was arrested on Saturday, a few hours after breaking out of the compound at Rafah, where people crossing from Egypt into Hamas Islamist-controlled Gaza are confined for a mandatory 21-day period.
He had been in the facility for less than a week and tested negative for the novel coronavirus after being apprehended, the ministry said.
In addition to the prison term handed down on Tuesday by a Hamas-run military court, the man was fined $700. It was the first time a jail term has been imposed in Gaza for violating restrictions aimed at stemming coronavirus infection.
The ministry gave no details on how the man escaped from the 500-room compound of single-story concrete buildings surrounded by a wall and guarded by police.
In its statement, the ministry said the man would also face drug-selling charges relating to membership in a narcotics gang.Health officials said 17 people had tested positive for the coronavirus in the Gaza Strip. The densely populated enclave is home to two million people.