Nick Meeks said he was working at his apartment on Cornish Street, in Kelham Island, when armed officers stormed the block of flats at around 5pm.
"I was sat there working on my laptop and there was a huge bang. I've never heard anything like it," said the 27-year-old medical representative.
"Naturally I popped my head out of the door and there was smoke billowing down the corridor and police in full armed gear pointing guns down the corridor shouting at me to get back inside my flat. You do what you're told when there's a gun in your face."
Mr Meeks said he was ordered to remain inside his second-floor flat at Daisy Spring Works for around half an hour before being allowed outside.
He told how the blast, which police said was down to the method used by officers to gain entry to the property, had caused extensive damage.
"There are cracks all the way down the corridor and huge cracks outside. It even blew a panel off the roof, whatever it was," he said.
"Within minutes of the bang loads of police had turned up and a cordon was set up. It was all very organised."
Residents of the block told shortly before 7pm how they were still not being allowed back inside, with police not telling them when they might be able to access their flats again.
Police said a man in his 20s had been arrested in Sheffield on suspicion of terrorism, and another man had been arrested in Huddersfield.
They said searches were being carried out at properties in both cities and the operation was not connected to last week's Manchester attack, in which 22 people were killed.
A police spokesman said: "Officers have today arrested two men from Huddersfield on suspicion of offences under Section 5 of the Terrorism Act.
"The men, age 24 and 29, were arrested at separate locations in Huddersfield and Sheffield
"Searches are being carried out in properties in Huddersfield and Sheffield.
"There are no connections to the recent incident and investigation in Manchester.
"The operation is based on recently received intelligence.
"We understand that people may have concerns as a result of this activity and we are grateful for the patience and understanding of the public while these enquiries are carried out.
"The public may have heard loud bangs at the time that police entered the property. We would like to reassurance you that this was part of the method of entry to gain access to the property."