The Molineux club have thanked supporters for their fine support in recent weeks and laid on the free travel to the Liberty Stadium as a gesture.
Nuno Espirito Santo's men will be backed by 4,700 away supporters in their Championship contest at Barnsley on Saturday.
Wolves and Swansea played out a goalless draw at Molineux last weekend.
Wolves managing director Laurie Dalrymple said: "The team has received in recent weeks, an enormous amount of support. It’s our feeling that we should be trying as frequently as we can to minimize the difficulties fans face in getting to support the team.
“After a busy schedule of games we appreciate this added expense, particularly at this time of year, so this initiative allows us to give some support back.
“Swansea is a long distance to travel on a Wednesday evening, particularly after a trip to Barnsley on Saturday, so we hope supporters take up this offer.”
Free coach travel is available for supporters when purchasing tickets. Tickets are on on sale to season ticket holders from Tuesday, January 9 (tomorrow), 10am.