Wilkinson, pictured, left Yarnton Road on Tuesday following his side's heavy 5-0 home defeat at the hands of Beaconsfield SYCOB on Bank Holiday Monday.
Wilkinson resigned after leading the Greens to the Hellenic League Premier title last season to win promotion to the EVO-STIK League Southern's Central Division One.
In a statement confirming his departure, Kidlington`s press officer Simon Dickens said: "Martin`s management team and squad have been contacted and a committee meeting will convene as soon as possible.
"Kidlington are indebted to Wilky`s dedication during his time with us, during which he achieved the club's long term objective to compete at Step 4, Southern League football.”
Former Bracknell Town number two Wilkinson left with Kiddy second from bottom having collected two points from their opening six games.
Wilkinson, who has also coached at Raith Rovers, Forfar Athletic and Swindon Town's academy, had also seen his side suffer an early exit from the Emirates FA Cup after losing to North Greenford United in the preliminary round.
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