While stood on the roof he then started throwing tiles, believed to have smashed the windows of at least three vehicles.
Police cordoned off the estate as hundreds of onlookers watched the drama unfold.
At one point 10 police cars, a fire engine and ambulance were on the scene along with a police negotiator.
Once he had been talked off the roof, he was arrested in connection with a public order incident at the address and a stabbing earlier in the day.
A statement from Humberside Police said: “At just before 6.40pm today (Thursday July 2) a 20-year-old man was arrested at an address on Burwell Drive, Grimsby.
“The man had previously taken to the roof of the property at around 2pm and there was concern for his safety.
“His arrest is in connection with a public order incident at the address and a stabbing earlier in the day at around midday in Grimsby, which resulted in a 28-year-old man requiring hospital treatment for non-life threatening injuries.
“Numerous officers attended to assist with enquiries into the stabbing and the subsequent incident involving the man on the roof.
“A 13-year-old boy was also arrested in connection with the stabbing and he remains in police custody assisting with enquiries.”
As police cordoned off the scene, they were faced with abuse.
At one time shouting was heard from the roof – telling police to move their patrol cars out of the street.
One unnamed eye witness said that the presence of so many police would only antagonise the situation.
He said: “He’s playing to the audience.”
Police officers at the scene during the afternoon had included an Operational Support Section and dog teams.
Councillor Jane Bramley, member for the South Ward, had been leaving her home for a meeting with police about incidents on the Nunsthorpe estate when she saw the police attending the initial stabbing incident.
She said: “I cannot fault the police. They have been really good.
“Since we have had problems down here they have been down daily.”