The college has been put on a "code red lockdown," according to police who are at the scene.
According to reports the college received a message stating there was a person with a weapon on the premises.
The Manchester Evening News has reported the alert came through a newly opened Twitter account.
Teachers and students at Bury College, on Market Street, have been told to stay inside.
The college is now being evacuated one building at a time.
Bury College is on lockdown after a "security threat" Live images: Bury college on lockdown Fri, March 24, 2017
According to reports the college received a message stating there was a person with a weapon on the premises
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Bury College in Bury, is being evacuated and police are on campus
Images show there is a large police presence outside the college.
Students have claimed some are “very worried” and “having panic attacks”.
Parents, meanwhile, say they have not been told what is going on.
One girl wrote: “Came to college to finish my coursework… now I'm locked in my class room on a red threat, bury college for you.”
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The scene outside Bury College in Manchester
Another Twitter user wrote: “Any info on what’s happening at Bury College? Why aren’t the student allowed outside?”
A parent said: "Daughter being evacuated now #burycollege bloody scary knowing there is nothing you can do to help."
The College had been visited in the morning by pupils from Sharples School in Bolton.
The school tweeted to say everyone had returned and is safe.
Bury College is currently on lockdown over reports of a person with a weapon
Coming live from bury college. Worrying scenes. pic.twitter.com/pEehzRl2hY
— lewis (@lewishamilton95) March 24, 2017
Police are maintaining a presence outside the college
A Greater Manchester Police statement said: “At 10.50am on Friday 24 March 2017 police were made aware of a threat made to Bury College, Market Street, Bury.
“Officers are in attendance to establish the full circumstances. A precautionary evacuation has been conducted.”
A spokesman from Bury Police later told the Manchester Evening News: “We are satisfied it’s a single strand piece of information that is not corroborated by any other information.
“We have some fast-paced enquiries ongoing to find the individual that has tweeted this threat and we will take robust action into the individual.
Police are at the scene of Bury College
Bury College has been placed on lockdown by police
“We don’t feel there’s any immediate risk to Bury College.
“But we are putting out additional resources to reassure the public.”
Students at Bury College began tweeting about the incident after being kept in classrooms.
Bury College principal Charlie Deane said there was a threat made to the college and police were called.
He said "nothing has materialised" but they are taking no risks and evacuating the college building-by-building.
Police are attending to a "security threat" at Bury College
A girl was stabbed in the face at the college in 2011 and needed 400 stitches after the brutal attack.
Surgeons had to battle to save the then 18-year-old's eye.
Police have said that there is a security threat at Bury College
The college said in a statement they were taking the threat seriously.
It said: “Please note, the college is currently investigating a potential threat to our security.
“We are in communications with the police, following their advice and have instigated our alert procedures as a precaution.
“We will update further as we receive more information.”
The leader of Bury Council Rishi Shori said police “have the situation under control”.
In a Twitter message he said students were asked to leave the building, which is across the road from Bury Transport Interchange and Bury Market.
Councillor Tamoor Tariq meanwhile said there was “lots of concern” but said on Twitter: “Please be assured, police have it all in hand and everyone is safe.”
Pupils from a high school in Bolton, Sharples School, had been on a day trip to the college.
The school tweeted: “All pupils who attended the trip to Bury College are now back at school.”
Greater Manchester Police have confirmed that the incident was triggered by a message on the social media site Twitter but that now the incident was "all concluded".
A spokesman for the police added that no one had been arrested and there were no injuries.