Crews remained at the scene on Barrack Street on Sunday morning after a fire tore through the Robertson’s building on Saturday.
The fire sent a large column of smoke over the city that could be seen from the opposite bank of the Tay.
At the height of the incident, nine fire engines attended the scene. Two remained on site on Sunday.
Detective Sergeant Stuart Martin, from Dundee CID, said: “This was a reckless and dangerous act of fire-raising, which has caused significant damage and disruption to the area.
“We have spoken with a number of witnesses and would appeal for anyone with information on the incident to come forward and assist our enquiries.”
The building on Barrack Street dates back to the 1930s. It closed as a furniture shop in 2011 and has lain empty for the past 11 years.
Firefighters worked “extremely hard” to tackle the blaze at an old furniture store in Dundee, the fire service has said.
A spokeswoman for the Scottish Fire and Rescue Service said: “We were alerted at 5:57pm on Saturday, November 12 to reports of a building fire on Barrack Street in Dundee.
“Operations control mobilised nine appliances and specialist resources to the scene and firefighters are working extremely hard to extinguish a large building fire. No casualties have been reported and crews remain on the scene.”
Residents shared pictures and footage of the fire on social media. Niall Campbell, who lives in Fife, said he saw the fire from across the River Tay.
He said: “I am on the other side of the Tay so quite far away, but can comfortably say I have not seen a fire of its scale in all my time here.”
A cordon was put in place, with police redirecting traffic as neighbouring streets were closed. Some crowds were seen gathering in the street as the fire raged on throughout Saturday evening.
Shona Robison, the SNP MSP for Dundee East and social justice secretary, praised the response of fire crews. She tweeted: “Such a shame to see the destruction of the once lovely Art Deco Robertson furniture store building in Dundee. Thoughts are with the emergency services working hard to get the blaze under control.”
Conservative North East MSP Maurice Golden said he hoped “everyone is safe”.
The derelict building had been on the market for years following its closure.