Officers were called just after 10.30am by the ambulance service after the man ? believed to be in his 20s - was found at a property on Fisher Street.
West Midlands Police spokeswoman Kate Baker said: "His death is currently being treated as unexplained and a forensic examination of the scene is currently underway.
"The man is yet to be formally identified but his next of kin have been informed.
"A post mortem will take place in due course."
One resident, who did not wish to be named, said ambulances had arrived at the scene first followed soon after by the police.
"Pretty much as soon as the police arrived they cordoned off the flats and it remained that way for hours," she said.
"It was strange as there did not appear to be any activity at the flat before the emergency services arrived."
She said there had been two ambulances at the scene.
Another resident said he had been shocked to wake up and see police vans outside his window.
"I wasn't aware anything had happened until I looked out and saw all the police,"he said.
"Given that the whole block has been cordoned off and the number of officers here it must be something very serious."
Another neighbour said she had returned to her home to see the cordon in place.
Residents said they did not know who lived at the flat.
A police tent went up outside the property at around 1.30pm and forensics officers could be seen entering and leaving the building as the investigation progressed.
Police and community support officers were stationed outside the block of flats.
Three police vans and an incident support unit were at the scene during the course of the day.