Male shoppers complained about being cat-called and followed by women, with most of the complains relating to verbal harassment, the Saudi Gazette reports.
The centre's security department says CCTV footage supports the men's claims. The videos have been handed over to the police for further investigation.
The newspaper suggests the men did not file formal complains because they feared "social stigmatisation".
Men interviewed by the paper suggested the solution was to enforce even stricter punishments and restrictions against women in public.
In Saudi Arabia, religious police enforce a strict policy of gender segregation, often harassing women who do not meet conservative standards of dress in public, according to a 2005 report by the US Human Rights think-tank Freedom House.
Like many Gulf countries, Saudi Arabia has no laws against harassment. Most cases go unreported by women, Al-Araby Al-Jadeed reports.
However, over the past two years Riyadh's Justice Ministry recorded 4,000 cases of sexual harassment.