The Richard III Society branded the decision as a "monumental mistake" which would be "humiliating" to the king.
However, the Very Revd David Monteith, Dean of Leicester, said the play would be "sensitive" towards him.
He was reburied at the cathedral in 2015 in a specially designed tomb.
The remains of the last Plantagenet monarch were placed under the cathedral two years ago, after they were discovered under a car park in the city in 2012.
Shakespeare's play is critical of the king, calling him a "poisonous bunch-back'd toad."
Philippa Langley, from the Richard III Society, is not against the play but is opposed to it being performed in Leicester Cathedral.
"To perform this play right beside this man's grave is quite frankly, a deliberate humiliation," she said.
"This is not what the great city of Leicester and its people is about."
Source: Royal Shakespeare Company
The Cathedral has said the show will go ahead as planned in July, despite the criticism.
"King Richard III lies in peace," Revd David Monteith told BBC East Midlands Today.
"What we now know is that he belongs to the whole nation and not just to one section of people particularly committed to his story.
"I've heard most people say how glad they are that Richard III, the Shakespeare play, will be performed here."
The play will also be performed at Peterborough, Ely, Gloucester, Bristol and Salisbury cathedrals in July.

He said he allowed the girl to marry a 26-year-old Lebanese man, in a ceremony in New South Wales, because he did not want her to have sex outside marriage.
The 63 year old was found guilty in April of procuring a child under the age of 14 for unlawful sexual activity.
During sentencing in Sydney the judge told him he had "failed" his daughter.
She said she hoped the punishment would act as a deterrent to others.
The father, who cannot be named to protect his daughter's identity, told Downing Centre District Court that he considered sex outside marriage a sin, so when his daughter reached puberty he decided she should marry.
When the Lebanese man, who was in Australia on a student visa, showed an interest, he arranged for a local sheikh to carry out the ceremony.
It took place last year in the Hunter Valley region, around 250km (150 miles) north of Sydney.
The marriage, which is not recognised under Australian law, was consummated at a hotel on the night of the wedding with the father's permission.
The pair also had sex at the father's home the following weekend. The court heard that the girl later had a miscarriage.
The man was jailed for seven and a half years in March for the sexual abuse of minor.
Australian authorities are now looking after the victim.
The judge told the court that religious beliefs did not justify the father's actions. "They were linked in the purpose that (the man) would have sex with his daughter," she added.
Leicester Cathedral has defended its decision to stage Shakespeare's Richard III a few feet from the monarch's final resting place.
[NEXT_CONCEPT]
An Australian man has been jailed for eight years for arranging an Islamic marriage between his 12-year-old daughter and a man twice her age.