Fly-half Laidlaw (shoulder) and fellow Scotland international Visser (leg) were injured in last weekend's opening 45-0 defeat to Saracens which leaves Edinburgh with work to do in Heineken Cup pool one.
Edinburgh back-row Netani Talei said: "The boys are still on a low at the moment because we didn't perform to the standard that this club demands. Every single individual involved with Edinburgh Rugby is hurting."
Edinburgh, semi-finalists last season, travel to Thomond Park seeking to revive their Heineken Cup campaign against two-time European champions Munster, who lost their opener to Racing Metro.
Talei added: "Munster will be too, and will be coming out twice as hard as last weekend because, like us, they want to stay in the competition.
"We need to regroup and recapture that buzz in the team. We need to pick ourselves up and work hard in training this week to improve for the next match, and work on our plans to beat Munster on Sunday.
"It has to be a good week for us. We need to re-set our minds and prepare our bodies physically for a very big challenge."