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Former Everton striker Ferguson oversaw the Toffees' 3-1 defeat of Chelsea last weekend after replacing Marco Silva, who was sacked following a comprehensive 5-2 Merseyside derby loss to Liverpool.
"Duncan Ferguson will remain as Everton caretaker manager for Sunday's Premier League visit to Manchester United," said a club statement.
"Ferguson will again be assisted by coaches John Ebbrell and Francis Jeffers and goalkeeper coach Alan Kelly."
Former Scotland forward Ferguson enjoyed two spells as a player with Everton, amounting to 10 years in total.
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He joined the club's academy as a coach under former manager David Moyes before moving into the senior backroom staff in 2014.
The 47-year-old's passion for the club was evident in the win over Chelsea, with many observers reckoning it had sparked a more committed display from a struggling Everton side.
Silva's 18 months at Goodison Park ended on December 5 after a Merseyside derby defeat that left Everton languishing in 18th place.
Moyes has been linked with a return to Everton and there has also been speculation that Carlo Ancelotti could be a target after the experienced Italian manager was sacked by Napoli on Tuesday.
Former Arsenal manager Unai Emery and Bournemouth boss Eddie Howe have also been suggested as full-time successors to Silva as has Manchester City assistant Mikel Arteta, a former Everton midfielder.
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