Officers were called to an incident in Princes Street, just down the road from the Cornhill, at about 12pm on Monday.
A spokesman for Suffolk police said a 26-year-old man was arrested on suspicion of possession of Class B or C drugs.
He also confirmed that a second 26-year-old man was arrested on suspicion of possession of class B or C drugs and possession of a knife or bladed article.
There was a large police presence in the town centre while officers attended the scene.
At least two police cars and a van were spotted alongside several officers in Princes Street.