Councillor Alan Mosley said that the party was instead targeting seats where it believes it is most likely to enjoy success.
The party has put 35 candidates up across the county, with a total of 74 seats up for grabs.
It currently has nine councillors.
The Conservative Party, which has been in charge of Shropshire Council, has put up candidates to contest all the available seats.
Councillor Mosley said: "We have chosen to concentrate our efforts on those seats where we have a real chance of success.
"We want to make a real effort in those seats where we have got strong support and make a success of it in that way."
The number of candidates being put forward means the Labour Group would not be able to command a majority on the council even in the unlikely scenario that it takes all the availaible seats.
However, Councillor Mosley, who himself is up for re-election as representative of Castlefields & Ditherington in Shrewsbury, said that the group hopes to join with other groups to oppose the Conservatives.
He said: "Given the demographic and opinion within Shropshire we have never considered that this time round Labour would be able to take control of the council but we are hoping to have an improved number of councillors and to join into partnership with other members who may jointly be able to form an administration that would rid the county of the destructive policies the Tories are imposing on it."
Councillor Mosley said he had also been impressed with the feedback candidates had been receiving while out canvassing.
He said: "We are getting an excellent response on the doorstep during canvassing across the area and people are recognising this is a local election and that Labour councillors have a record that is second to none in terms of commitment."