The sign outside Chimes cafe in Machynlleth, Powys, says: "The more you weigh, the harder you are to kidnap! Stay safe. Eat cake!!"
April, five, went missing on 1 October 2012 near her home, sparking the biggest search in UK history.
The cafe's owner said the sign was not meant to be distasteful or offensive.
She added the sign had been on "display for many weeks" and she had "only received one comment".
"April Jones's family have been in here recently, when the sign was up, and have not said anything," she said.
However, she admitted she could "appreciate how others would interpret the message", but believes those who have complained "have taken it the wrong way".
Machynlleth resident, Angharad Penrhyn Jones, took to Twitter to say: "A sign outside a cafe in #Machynlleth: "The more you weigh, the harder it is to get kidnapped. Eat cake!" In view of #AprilJones, shocking.
"I went to talk to cafe owner and apparently the sign is 'humorous' and the kidnapping happened 'years ago', and I am being 'hypersensitive.'
Author and former parliamentary candidate, Mike Parker, said: "I think the sign is totally inappropriate and my first thought was how distasteful it was considering what had happened previously in the town".
The cafe is situated behind the landmark clock tower in Machynlleth, which played a prominent visual role during the search for April when a large pink ribbon was placed on the railings outside.
Mark Bridger, 47, of Ceinws, Powys, was found guilty of abducting and murdering April in a sexually motivated attack and must spend the rest of his life behind bars.
Her remains have never been found.

Thieves took the animal from Silver Star Pets in Pengam, along with dog leads, dog coats, fish tanks, pet food and dog grooming equipment worth £35,000.
The incident is one of four break-ins that occurred at the Britannia Enterprise Centre some time between Tuesday evening and Wednesday morning.
Police are appealing for information.
The other units broken into were Auto Stitch, George Monumental Masons and Pride and Groom where damage was caused to the doors but nothing was stolen.
A taxi sign, however, was also stolen from one of the vehicles parked at the centre.

Poysden and Mellor, both 25, have committed to the Bears until at least the end of the 2018 season after five Championship games each this summer.
Warwickshire chief executive Neil Snowball said: "Josh and Alex have big futures here at Edgbaston.
"They played important roles in 2016 and proved that they can compete at the highest level of the domestic game."
Poysden, who was already tied to Edgbaston to the end of 2017, has worked with the England Lions at the National Cricket Centre in Loughborough this autumn and is currently with the Lions squad at their training camp in Dubai.
He has made 16 one-day and 19 T20 appearances for the Bears since initially joining on trial after leaving Cambridge University ahead of the 2014 season.
He also made a late-season breakthrough in the County Championship this summer, taking 15 wickets in his five appearances, including a career-best 5-53 against champions Middlesex at Edgbaston.
Former Staffordshire player Mellor, who first joined the Bears at the end of the 2015 season on a one-year deal, has now signed a new two-year contract.
Mellor, whose late-season Championship appearances came as cover for the injured Tim Ambrose, has also played three limited-overs games.
Warwickshire are still without a director of cricket following the departure of Dougie Brown in October.
They have been strongly linked with a return to Edgbaston for former Bears boss Ashley Giles, who is still contracted to his current county Lancashire for another year.
BBC Sport understands that negotiations remain ongoing with Lancashire over Giles, who still lives in the Midlands.
Chief executive Neil Snowball reiterated last week that they would like to make an appointment before Christmas.
A cafe owner has defended a sign urging people to eat cake to avoid being kidnapped in the town where April Jones was abducted and murdered in 2012.
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An African Grey parrot valued at £900 has been stolen from a pet shop in Caerphilly.
[NEXT_CONCEPT]
Warwickshire leg-spinner Josh Poysden and wicketkeeper Alex Mellor have signed contract extensions.