Council leader Peter Nutting said the authority would be looking to secure the redundancies through people retiring, leaving for new jobs, and voluntary redundancy.
"We are likely to lose 200 positions from the council in the next year or so," he said.
Councillor Nutting said the authority would be able to cope with the losses due to its investment in a new IT system.
He said: "We are investing around £20 million in a computer system which will result in more efficient working in the back office."
The news comes as the leader revealed that the authority wants to raise council tax by nearly six per cent this April.
The move will not be blocked by opposition councillors who say they see it as the only way to protect vital services.
The proposed 5.99 per cent increase, up from the rise of 3.99 per cent last year, is being considered to help Shropshire Council tackle its multi-million pound finance problems.
Labour leader, Councillor Alan Mosley and Liberal Democrat leader, Roger Evans, have said they will not oppose the plans.
"We're not going to oppose the increase where it is to protect vital services," Councillor Mosley said. "But it just goes to show the absolutely disastrous state of Shropshire Council's finances due to government policy of austerity backed by the council administration.
"This is just the start and it's the price council tax payers are going to have to pay for a diminished amount of local services."
"The blame lies with the Tory government which the Shropshire Council administration supports and represents locally."
The rise, which is double inflation, would represent £75.45 a year more for Band D properties, and £58.68 for Band B homes.
The authority would only be able to increase council tax to 5.99 per cent because of changes to government policy. The increase would be made up of 2.99 per cent for the council, as permitted by government, added together with three per cent, to pay solely for the costs of providing adult social care.
Councillor Evans added: "The proposed rise shows the way that the money has been managed by the present administration. But the council needs income in order to deliver its legal services like safeguarding and adult social care.
"I'm further disappointed that the budget papers are still not in the public domain because it means those outside the cabinet are not really aware of why this is being proposed."
Councillor Mosey warned the "black hole" in the local authority's finances could get worse when the council invests in three Shrewsbury town centre shopping centres - a scheme which was backed by full council last month.
He added: "That black hole could get even worse given that some of the returns rely on highly risky things Shropshire Council should not be investing in like shopping centres."