The get-together got under way at Glasgow's Scotstoun Stadium on Monday morning as head coach Scott Johnson prepares his side for November's viagogo Autumn Tests against Japan, South Africa and Australia at Murrayfield.
But Edinburgh wing Visser sustained a leg injury in his club's RaboDirect PRO12 victory over Treviso on Friday.
He will undergo an MRI scan at SPIRE Murrayfield Hospital on Monday night and is in the care of the Edinburgh Rugby medical team and consultant John McKinley.
Meanwhile, Saracens centre Taylor suffered abdomen and shoulder damage in his club's match against Northampton at the weekend and is being treated by the Allianz Park medics.
Back-row forward Blair Cowan and hooker Scott Lawson also sat out Monday's contact training as they played for London Irish and Newcastle respectively 24 hours earlier at Kingston Park.
A number of other players will also take a limited part in training as a consequence of "bumps and bruises", the Scottish Rugby Union has confirmed.
- Sports & Recreation
- Edinburgh Rugby