Wolves midfielder Edwards has missed the last seven internationals due to a back problem, but recently returned to the starting line-up at Molineux and comes straight into the national squad for their final Euro 2012 qualifiers.
QPR defender Gabbidon is out due to a knee injury picked up in their win over Wolves, while Cardiff striker Earnshaw, whose close-range miss denied Wales a point at Wembley last time out, has a thigh problem.
Despite only picking up their first points of the campaign against Montenegro last month, Wales can still finish in third place in Group G with positive results against the Swiss in Swansea and against Bulgaria in Sofia.
Sam Vokes is included in the 23-man squad in Earnshaw's absence while defender Neal Eardley drops on to the standby list.
Liverpool striker Craig Bellamy and Sunderland midfielder David Vaughan are available again after missing out against England due to suspension as Wales look to continue the progress they made in last month's double-header.
The win over Montenegro and narrow defeat at Wembley have seen Speed's side climb 27 places in the FIFA world rankings, up to 90th from a record low of 117th.
Wales squad for the Euro 2012 qualifiers against Switzerland and Bulgaria:
Hennessey (Wolves), Myhill (Birmingham), Blake (Cardiff), D Collins (Ipswich), J Collins (Aston Villa), Gunter (Nottingham Forest), Matthews (Celtic), Taylor (Swansea), Williams (Swansea), Allen (Swansea), Bale (Tottenham), Collison (West Ham), Crofts (Norwich), Edwards (Wolves), King (Leicester), Ledley (Celtic), Ramsey (capt, Arsenal), Robson-Kanu (Reading), Vaughan (Sunderland), Bellamy (Liverpool), Church (Reading), Morison (Norwich), Vokes (Wolves).