Demolition work is due to begin at the Dryburgh Resource Centre site and is expected to last 16 weeks.
The Napier Drive building, which formerly housed the Connect 5 off-site education centre, will start to come down on January 22.
The works will cost the council more than £152,000.
A resident who lives on Napier Road said: “I am disappointed it is coming down.
“However, it depends what the area will now be used for and if it will be beneficial for the community.
“The residents nearby have not been kept informed by the council.
“I only found out last week that it was to be demolished.
“We should have been given more information about what the plans were for the building and the demolition.
“It is also worrying that traffic is already quite bad in the area and I think the site traffic may add to that.
“However, if the work has to be done, it has to be done.”
The demolition comes after Dundee City Council merged three off-site education centres — Connect 5 based at the Dryburgh Resource Centre, the Castlepark Centre on Dudhope Terrace and Balerno, at the Happyhillock Child and Family Centre — into one site at the Rockwell Primary School building in Lawton Road.
The move was expected to save the authority £510,000.
Previously Councillor Stewart Hunter said: “By merging, we can find a saving by doing something beneficial for those involved in the service.
“The original rationale behind the plans was that the three current buildings are of poor quality.
“And, given that we have spent a lot of money on Rockwell, common sense says we should use it.”
A Dundee City Council spokesman said: “We will be working to ensure that disruption is kept to a minimum.”