Announcing the party's candidates for the forthcoming poll, Mrs Foster said she was "quite sure (Mr Robinson) will be returned."
Mr Robinson won back the seat in the 2015 election from the Alliance Party's Naomi Long, who unseated the DUP's former first minister, Peter Robinson, in 2010.
Ahead of next month's election there had been speculation about a unionist deal covering seats like South Belfast and East Belfast, where there was a unionist pact two years ago, in which only a single candidate for the two parties stood in either constituency.
However, the DUP and UUP have been unable to conclude a pact ahead of the General Election.
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Mr Robinson will be up against Ulster Unionist Hazel Legge, a Lisburn and Castlereagh councillor.
"If you want a unionist candidate in East Belfast then you have to vote for Gavin. The Alliance candidate is not a unionist and she has said so herself. I am quite sure he will be returned," said Mrs Foster.
In South Belfast Emma Little Pengelly, who lost her seat in the Assembly election, has made a return to front line politics to try to take the seat from the SDLP's Alasdair McDonnell.
DUP veteran Jim Wells will not be standing in the election for personal reasons.
The former health minister told the Press Association that due to health problems within his family he has decided to take a break. However, he will remain as an MLA.
Mr Wells has been the DUP's South Down Westminster candidate on the past four occasions. He has unsuccessfully fought five previous general elections - Upper Bann in 1983 and in South Down in 2001, 2005, 2010 and 2015.
Diane Forsythe has been selected to stand in South Down.
Despite the absence of a unionist pact the DUP gave the UUP's Tom Elliott a free run in Fermanagh and South Tyrone and the Ulster Unionists returned the favour in North Belfast, where Nigel Dodds will fight to hold his seat. Both unionists will face strong challenges from nationalist Sinn Fein candidates.