The assault happened around 4am at the flat on Gorgie Road on Tuesday.
Officers say two men entered the property with their faces covered and assaulted the pair.
A 29-year-old man was taken to Edinburgh Royal Infirmary with non-life threatening injuries. The woman suffered minor injuries.
Detective Constable Joyce Gunderson, of Corstorphine Police Station, said: “This incident happened in the early hours of the morning however it’s possible that passing traffic, especially taxi drivers, may have noticed the two men leaving the property.
“If anyone remembers seeing two men acting suspiciously outside around that time, please get in touch.”
Those with information can contact Police Scotland on 101 or alternatively the charity Crimestoppers anonymously on 0800 555 111.