Sainsbury's potato buyer John Maylam has been arrested on suspicion of receiving payments from a UK supplier.
Maylam was questioned by police after claims he took what is thought to amount to £3 million from Greenvale AP.
A member of staff at Greenvale has also been arrested and questioned.
The supermarket notified police after being alerted to the problem by Greenvale.
The two men were arrested on suspicion of corruption and money laundering and subsequently bailed.
Greenvale supplies about half of Sainsbury's potatoes and has packing operations in Shropshire, Cambridgeshire and Berwickshire.
A number of staff have been suspended following an internal investigation, it has been reported.
A Sainsbury's spokeswoman said: "We can confirm that allegations have been made concerning certain payments and benefits by a supplier to an individual employed by us.
"We have the highest standards of corporate governance and following inquiries have passed our findings to the police for further investigation."
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