The incident happened at about 7.30am in Gillygate and the scaffolding completely blocked the road near the junction with Bootham. Nobody has been injured, North Yorkshire Police said.
The scaffolding was erected outside the Sound Organisation shop in Gillygate.
City of York Council asked people to avoid the Gillygate and Bootham area while emergency services were at the site, but the road and footpaths have now fully re-opened.
It caused major traffic delays around the centre of York, with many motorists using alternative routes rather than heading towards Gillygate. Rougier Street was among the roads that had heavy traffic as a result.
Police were at the scene for several hours and questioned witnesses. City of York Council contractors were also at the scene to clear-up the scaffolding.
A member of staff at Betfred on Bootham, said: "All I heard was a massive bang, one of our windows has been smashed by the scaffolding.
"Something needs to be done about this corner, it's a nightmare, the road is always busy, it's always busy round here.
"My cashier says a bus clipped the scaffolding the other day.
"We will be open today as usual."
Lizzi Healy, who works at Croque-Monsieur, said: "A few customers witnessed it. They said a truck had caught the corner of the scaffolding and pulled it down.
"It's lucky there was nobody underneath.
"It happened between 7.30am and 8am."
A man who works for Transdev, who didn't want to be named, said: "It's an accident waiting to happen. My drivers have seen a couple of lorries come round and clip the scaffolding. It's a bit tight for the bigger lorries to get round.
"It's very lucky nobody was hurt."
Neil Ferris, City of York Council's director of economy and place, said: "We are relieved that no-one has been injured and thank everyone for your patience with this matter. We are working with the police and will work with any health and safety investigation and have confirmed that the building is safe.
"We have reopened pedestrian access, are working to repair the damaged traffic light and are ensuring the scaffold is removed so the road can reopen."
Findley Roofing and Building has been carrying out work on the grade II listed building where the scaffolding was erected.
Grant Findley, managing director of the firm, said: "We sub-contract scaffolding out.The scaffolding was by another company.
"It is a lorry that has struck. I don't think any scaffold would stand being hit by a lorry or wagon, that appears to be the reason it has come down. The scaffold has been up for about four weeks.
"We were due to hand over this week. All the new roof and all the high level stuff has been done. There were some windows left to paint."
He added: "We are just thankful nobody has been hurt.
"The foreman was on his way to the site with his team. They hit a bit of traffic and were late by about five minutes. They just missed it."
Mr Findley claims no-one has reported any problems with the scaffolding while it has been up.
A spokeswoman for North Yorkshire Police said: "Collapsed scaffolding caused traffic in Gillygate from around 7.30am on Monday.
No-one has been injured.
"Police officers assisted at the scene and City of York Council is managing the incident."
"It is not a police matter."