Menzies said rectifying "operational issues" at the airport would cost an extra Â£6m in the second half of 2015.
It warned full-year profits could be Â£2m lower than previously forecast.
However, it reported strong profit growth at its US hubs, while its distribution arm was "delivering ahead of forecast".
In a trading update for the 10 months to 30 October, Edinburgh-based Menzies said: "Within the aviation division, service levels at London Gatwick have been restored.
"However, the actions we have put in place to mitigate the operational issues and deliver the customer's operational requirements will cost Â£6m of additional investment, mainly in manpower, in the second half of the year, and will impact this year's earnings.
"Contract negotiations with this customer continue, and we are working towards a resolution before the year end."
Menzies said its aviation division continued to perform well in all regions outside the UK.
Ground handling turns and cargo tonnes were up 9% and 4% respectively, with revenue in the period up 6% on last year.
Chief executive Jeremy Stafford said: "During a busy period of transition, we continue to progress with the group's strategic objectives.
"Our distribution business is quickly gaining traction in the UK e-logistics market, whilst continuing to deliver cost and cash improvement initiatives.
"Aviation continues to benefit from growth in the Americas, whilst we continue to work through UK operational matters.
"I am disappointed that contractual issues at London Gatwick have led us to revise our aviation outlook for this year, albeit largely offset with strong progress in our distribution business.
"The group remains well placed to drive earnings."

The Most Rev Justin Welby told worshippers at Canterbury Cathedral that the attacks risked "causing us to act fearfully, to see a world in which fear triumphs".
But he also said: "On Easter Day hope decisively overcame fear".
Tuesday's bombings in Brussels killed 28 people and injured dozens.
The archbishop said hope can seem far away and fear so close "in the shadow of this week's darkness".
"Fear is reasonable, a normal human reaction," he added.
Pope delivers Easter message of hope
PM praises UK's 'Christian values'
"Easter proclaims to us in flesh and blood that fear and death and terror are not the last words.
"God has spoken life, hope and purpose.
"Terror speaks of a world at war with itself, of faiths at each others' throats.
"Jesus Christ reaches out not in exclusion but in embrace; this is the feast of the victory of God, and we celebrate in the midst of darkness, by our worship and praise shining an unquenchable light."

The girl, called Nieve, was attending the Handmade Parade in Hebden Bridge on Sunday with her grandparents when the dog jumped up and bit her.
She needed eyelid surgery and suffered "potentially irreparable damage" to a tear duct.
The man in the e-fit is described as being broad, bald and aged about 50.
A second man, also thought to be about 50 and of similar build, was present at the time of the incident, West Yorkshire Police said.
Both men left the scene without checking on the girl's welfare or leaving any details.
The dog, believed to be a Staffordshire bull terrier, was on a lead at the time of the incident and is described as brindle and white coloured.
PCSO Gareth Helliwell said: "The five-year-old girl involved in this incident needed reconstructive surgery to an eyelid following this attack and has suffered potentially irreparable damage to her lower tear duct."
The girl's family described the dog's owner as "scum", adding "she could have lost her eye, she was covered in blood and the guy just ran off, it's cowardly".
She was also bitten on the ankle despite the dog being pulled away on a lead, they said.
Police appealed for anyone with information about the dog or the two men with it to contact them.
Logistics group John Menzies has issued a profits warning following problems with its ground handling contract at London Gatwick Airport.
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The Archbishop of Canterbury has warned people not to give in to fear after the attacks in Brussels, in his Easter Sunday sermon.
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Police have issued an e-fit of a man they want to trace in connection with a dog attack on a five-year-old girl.