The club has refused to discuss the full reason for the ban, although newspaper reports have suggested it followed an altercation in a Western London pub.
"London Wasps have suspended Andy Powell and Tim Payne with immediate effect pending an internal investigation," read a statement on the club's website.
"The club is not in a position to disclose any further details at this stage and will not comment again until the internal investigation has concluded."
Newspaper reports appear to be backed up by a Metropolitan Police statement which read: "Officers were called at 22.30 to reports of an altercation at the Walkabout Public House on Shepherds Bush Green, W12.
"An incident is being investigated by officers from the violent crime unit at Hammersmith and Fulham police. No one has yet been arrested and our enquiries are ongoing."
Powell, who featured five times for the 2009 Lions in South Africa, is currently sidelined with injury while Payne played in Wasps 51-18 win over Leeds on Sunday.
Powell is the second Welsh international to be suspended in 24 hours after Gavin Henson was disciplined by Toulon following an unrelated incident.