Hundreds of public squares, streets, libraries and schools across Egypt are named after the couple.
Mr Mubarak's 29 years in power ended with his resignation in February after weeks of mass anti-government protests.
The 82-year-old is currently under arrest at a hospital in the Red Sea resort of Sharm el-Sheikh.
He is due to be questioned about allegations of corruption and alleged violence against protesters during the popular uprising.
Egypt's state news agency Mena reported on Thursday that his health is "unstable".
Portraits of the former president have already been taken down at public institutions across the country.
Ordering the same to be done for the Mubarak name, Judge Mohammed Hassan Omar said: "It has become clear that the size of the corruption that's being uncovered every day exceeds by far anyone's imagination."
After the ruling, the transport minister said the Mubarak name would be removed from all ministry facilities, including a major underground station in central Cairo.
There are suggestions for streets to be renamed after the people who were killed in the recent anti-government protests, the BBC's Yolande Knell in Cairo reports.
An Egyptian government fact-finding panel reported recently that at least 846 people were killed and 6,400 were injured during the 18 days of protests earlier this year.
The mission - consisting of a panel of judges - said security forces fired live ammunition, placed snipers on rooftops and used vehicles to run over protesters.
Mr Mubarak's two sons are among a growing number of ministers and officials from his ruling circle who are also facing investigation.
A court in Egypt has ruled that the names of ousted President Hosni Mubarak and his wife Suzanne be removed from all public places.