The party's selection process is expected to take around a month – with candidates first placed on a 'long-list', before being whittled down to a shortlist and then put to the Constituency Labour Party (CLP) members for a vote.
Paul Forrest, the chairman of Shrewsbury & Atcham CLP, said they were expecting considerable interest in the position.
He said seat was attractive to candidates due to opinion polls showing a possibility of Labour win in the constituency – despite it being a Tory stronghold.
Nominations close at midday on Thursday, June 1.
The Conservative Party re-selected current Shrewsbury & Atcham MP Daniel Kawczynski as its candidate at a meeting earlier this year.
Mr Kawczynski was first elected in 2005 and has won the seat a total of five times – most recently with 31,021 votes, an 11,217 majority over second placed Labour candidate Julia Buckley, who polled 19,804 votes.
Councillor Buckley had been drafted in at short notice after the CLP removed its long-standing candidate, Laura Davies, just weeks before the election.
The Liberal Democrats have selected Shropshire councillor Alex Wagner as their candidate for the election.
Mr Forrest said: "We have already had a lot of informal interest but expect quite a broad array of candidates, both strong local candidates and some interest nationally.
"It is seen as a very winnable seat."
Mr Forrest pointed to a forecast from the Electoral Calculus website, which makes predictions based on previous results and current opinion polls, that Labour has a 75 per cent chance of taking the seat.
He added: "We want to select not merely a good candidate but someone who will make an exceptional MP, who will represent the constituency wholly and fully."