Justice Secretary Humza Yousaf told The Nine staff absences due to the rate of infection had put a major strain on the Scottish Prison Service.
Mr Yousaf described the situation as "increasingly alarming".
He added: "I cannot envisage a time when we do not release prisoners to make that a safer environment.
"So I am actively looking at the options we have to do that."
The justice secretary said options included home detention curfews, where prisoners were released and monitored by electronic tagging instead.
He said: "But we may need to look at what sort of powers we need to do some sort of emergency release as well.
"That is all being proactively explored as we speak."
Asked about the timescale, Mr Yousaf said: "It could happened as early as next week.
"I am not committing to that but, certainly, the situation is increasingly alarming, for me increasingly concerning.
"I would be surprised if in one way, shape or form we did not look to release prisoners and do that relatively urgently."
Mr Yousaf stressed the authorities would adopt a measured approach.
He added: "To reassure the public this would be done with the appropriate risk assessments in place.
"We are talking about people who would potentially be toward the end of their sentence anyway."
Earlier the SPS published updated information on its website for families and visitors in light of the pandemic.