They posed on the roof of one of the college's London Road buildings for more than five hours with a banner that said "No more lockdown".
One of the men was wearing white overalls and what looked like a gas mask, while the banner also had a logo very similar to that of independent girls school Shrewsbury High.
Police officers were called to the scene to attempt to talk the protesters down.
Shortly before 7pm the two agreed to come down after demanding to speak to the media.
The pair were then arrested on suspicion of causing criminal damage.
The Shropshire Star has been sent screengrabs from the Facebook page of Add Woods who appears to be one of the men on the roof.
He posted photos and videos showing his view, including one where police officers can be seen on the top of the building opposite.
It comes after numerous posts in a Shropshire Facebook group calling on people to rebel against the regulations, which mean you are only allowed to leave your home to buy essentials, exercise once a day or commute when not able to work from home.
The private Shropshire Corona Resilience Network group has more than 500 members and claims to be "dispelling fear with facts" while sharing numerous unsubstantiated conspiracy theories.
London Road was completely closed to traffic while the incident continued.
A West Mercia Police spokeswoman said: "Police were called around 1.10pm to reports of two men on the roof of Shrewsbury College in London Road in Shrewsbury."