Timpson was among several MPs in child and youth-related government roles who failed to win re-election to parliament. He lost his Crewe and Nantwich seat by just 48 votes to Labour's Laura Smith.
Tim Loughton, who Timpson replaced as children's minister in 2012, said: "It's a loss. He took over from me and did a very good job."
Loughton said he believes an announcement on Timpson's replacement may be made "later today or tomorrow".
"In terms of where we go from here and who replaces him it's a little bit premature," he added.
"I don't want to speculate on that until we've got something. I'm sure she [Prime Minister Theresa May] will want to get on with it."
In addition to Timpson, Rob Wilson, who was appointed youth minister in 2014, also lost his Reading East seat to Labour's Matt Rodda with a 16 per cent swing.
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