Some stores are understood to have seen sales come under pressure after the group was forced to rely on reserves of vouchers when security print firm BemroseBooth called in administrators in June, according to a report in Retail Week magazine.
The blow came at a key time for voucher sales, during the summer wedding gift season.
One Waitrose employee reportedly wrote to the group's in-house magazine The Chronicle complaining that their store had run out of vouchers: "Our branch can sell up to 1,500-plus in gift vouchers a week, but we have none.
"So not only are our sales affected, but so is our bonus, which is beyond our control."
John Lewis said it had experienced "difficulties" with its supply of gift vouchers. But it said the situation had been mitigated through the use of vouchers held in stock.
A spokeswoman confirmed that none of the John Lewis department stores had completely run out of vouchers, but Waitrose has had to switch stock of vouchers between stores due to the supply crisis.
The group said: "This situation has been mitigated by the use of reserve stock kept on hand specifically for such purposes and as a result we have been able to continue to meet customer requirements.
"We are pleased to say that we have found another supplier and hope to have new vouchers available shortly."
BemroseBooth has recently been sold by administrators, although two sites in Derby were closed, ending its history in the city dating back more than 180 years. Paragon Group bought the two remaining offices in Hull and Thornaby in Teesside in July and the business has now been renamed BemroseBooth Paragon.