Ulf Kristersson has admitted he knew Peter Magnus Nilsson had broken the law before appointing him last October.
The aide's behaviour was "stupid", but did not mean Mr Nilsson was unsuitable for the job, the PM said.
The opposition Social Democrats are calling on Mr Nilsson to resign.
The centre-left party's justice spokesperson Ardalan Shekarabi told public broadcaster SVT it was unacceptable for a chief aide of the prime minister to lie to the police, given "the problems we have with serious crime in Sweden".
Peter Magnus Nilsson, a finance journalist turned prime ministerial aide, was appointed after Sweden's new centre-right coalition government took office in October 2022, backed by a far-right party.
The illegal eel fishing incident took place a year earlier, in 2021, on an autumnal day off Sweden's southern coast.
It is against the law to go eel fishing in Sweden without a permit. The European eel, a local delicacy, is critically endangered according to the Stockholm University Baltic Sea Centre.
In a Facebook post, Mr Nilsson said he had been trying to sort out his equipment and throw small eels which had been caught in his fish-traps back to sea.
According to an official report seen by SVT, Mr Nilsson had four traps containing 15 eels, weighing 11kg (24lb) in total.
Marine officials apprehended him and asked if the equipment was his, but he said it was not.
Over a year later, a "friendly man" from the local police force called, Mr Nilsson says. Once again, he denied possession of the traps.
He later called the police back to correct his statement, he adds, and has now been fined 38,800 kronor ($3,800; £3,060).
"I am extremely sorry about all of this," Mr Nilsson said, admitting it was "inappropriate" to neither own up during the incident nor the following year.
Speaking to SVT, Prime Minister Ulf Kristersson was critical of Mr Nilsson not telling the truth immediately, but argued that was weighed up by his subsequent admission and acceptance of the fine.
Mr Kristersson has now been reported to the parliamentary committee that reviews ministerial behaviour.
The Social Democrats are seeking details on the process of Mr Nilsson's appointment and security clearance.
The committee will review the case over the next few months.