Director of places Tom McCabe and head of finance and commerce Rachel Musson drew a combined annual salary of more than £210,000.
They both left the authority recently as part of a management shake-up.
The council's information governance team today refused a Freedom of Information request from the Shropshire Star – claiming it would be 'unfair' to reveal what pay-offs they were given.
While the Star has lodged an appeal against the decision, the figures will now not be made public until they are published in Shropshire Council's annual accounts, expected in June or July after May's local elections.
The response to the FoI request did reveal no payment was made to head of business improvement Wendy Marston, who also left the authority recently, resigning to take up a position with a different council.
Mr McCabe, who was paid £131,355 a year, left the authority on December 31, with Ms Musson, who was on a salary of £85,000, leaving at the end of January.
A spokesman for Shropshire Council said: "The council considers it unfair to the individuals concerned to have any payments made public as they have only just left the authority. This information is therefore considered exempt from disclosure."