The incident at the former Book Centre in White Abbey Road, Bradford., caused outrage on social media.
Police have confirmed they attended a disturbance, and are looking into the matter.
The Book Centre has closed down and the new owners have given the previous owners a month to move out the stock, which included a number of Qurans and other Islamic books.
A spokesman for The Book Store said some Islamic literature had been put in a skip, but denied that included any Qurans.
He said: "It has come to our attention that some Islamic materials were found in a skip next to Book Centre.
"While the Book Centre site is being cleared, no Islamic material of any sort was purposefully disposed of.
"A small workforce was instructed to clear two storerooms from which some material made its way into the skip.
"This is wrong, unacceptable and a genuine mistake.
"The skip will be looked at as a matter of urgency and any materials removed.
"We take such matters very seriously and would like to reconfirm that this has been a genuine mistake on the part of those filling the skip after repeated advice and guidance by the proprietor as to what material must not be thrown away."
The spokesman also criticized a "group of individuals" who arrived at the store during the afternoon of "harassing and bullying" the shop's 80-year-old former owner, who was "not responsible for the filling of the skip".
"The store rooms were cleared by non-Book Centre staff who were given clear direction as to what they were meant to do and how they were meant to do it.
"What has happened here is a case of genuine human error, we are really disappointed."
The spokesman also said people "not associated with the Book Centre" had been entering the premises and removing Qurans and other property.
The incident has been reported to the police.
Reacting to images and posts uploaded on social media last night, a spokesman for Baker Reign Solicitors, which represents the new owners, said: "The board of directors of our client are very conscious that the Holy Quran needs to be treated with the utmost respect particularly as they are practicing Muslims.
"Our client therefore condemns the treatment and mishandling of the Holy Quran in such an obscene manner.
"Should our client have been aware that the previous owner would have sought to dispose of the Holy Quran and other books in this manner they would have assisted in distributing the books to various Mosques throughout the city.
"Our client now hopes that the previous owner takes a more responsible course of action by distributing the books to those less fortunate and in need of Islamic guidance”.
A spokesman for West Yorkshire Police said: "Police were called to commercial premises in White Abbey Road at about 3.19pm yesterday, following reports of males shouting and abusing staff.
"The caller said they were clearing out a stock room and had been accused of throwing away Islamic literature.
"Officers attended and spoke to the males who said they had suspicions Islamic literature was being put in a skip.
"Police were called to the premises again at around 6pm after reports of theft from the premises.
"Enquiries are continuing today to establish the circumstances."
Source: The Telegraph and Argus