The Pyramid Centre in North Bretton and Age UK building in Lincoln Road are being sold for nearly £1 million by the city council.
The cash-strapped council, which is currently tackling a £28 million deficit, agreed the sale of both assets through an auction on Tuesday.
Discussions are now taking place with the buyers to finalise the sales before April.
The Pyramid Centre is a retail unit which contains The Oxcart pub, Premier Late Shop, two takeaways and two buildings leased to Bretton Parish Council.
Council chair Catherine Lee said there were concerns about the future of the convenience store as losing it would be a “huge problem for the elderly people who live nearby.”
However, a council spokeswoman said: “Current lease arrangements will remain the same for existing leaseholders.” She added: “We regularly review buildings, land and other assets in our ownership and sell those that are in the city’s financial interests to do so.
“Money that we generate from selling such assets is then reinvested into providing services for residents.
“The decision was made to sell The Pyramid Centre and the Lindens [Age UK building] as both sites will require significant investment in future years.
“At a time when council budgets are reducing, we cannot commit to being able to invest in these sites so a decision was made to sell them.”
The two sales brought in £930,000, with the Pyramid Centre sold for £492,500 and Lindens for £437,500 after an auction by Allsop. The names of the winning bidders have not been revealed.
The parish council said it was disappointed it had not been given notice of the auction and claimed it had only found out because a surveyor came out to take pictures.
But the council spokeswoman said: “Tenants, ward councillors and Bretton Parish Council were written to in January with details of the plans and auction date.”
The centre was due to be sold before March 2018 but this date was brought forward.
Age UK Cambridgeshire and Peterborough has a lease on its building until April 2021. Its services include support with homes and gardening, while it runs a befriending service and day care services.
Gloria Culyer, chief executive of Age UK Cambridgeshire and Peterborough, said: “It’s a case of business as usual. Our work is unaffected.
“The base for Age UK in Peterborough has been at the Lindens for many, many years and we are looking forward to things continuing and us developing our work with older people in Peterborough.”