Zakir Naik, who is listed on the website of the Islamic Research Foundation International as its chair, was barred from entering the UK in 2010 because of his views, which include praising Osama bin Laden and saying all Muslims "should be terrorists".
The regulator said it had disqualified Naik as a trustee in April this year, but he had challenged the decision at the charity tribunal.
Last month the satellite channel Peace TV Urdu, which Naik founded in 2009, was taken off air after the regulator Ofcom ruled one of its programmes had incited murder.
This prompted the society to urge the commission to take action against the charity, which advances Islam and generated income of £518,000 in the financial year ending 31 January 2019.
The society submitted a request to the commission under the Freedom of Information Act, which revealed that the regulator had received five complaints about the charity between 1 January 2010 and 31 October 2019 but had not opened any statutory inquiries.
The NSS said it welcomed the commission's attempt to disqualify Naik from trusteeship, but questioned why there had been no statutory inquiry into the IRFI itself.
Megan Manson, campaigns officer at the society, which promotes secularism, said: "It’s concerning that the commission has not opened an investigation into Islamic Research Foundation International, given its appalling track record.
"There appears to be a compelling case that IRFI doesn’t serve a public benefit and is therefore not deserving of charitable status."
Manson also urged the government to review religion's place in charity law.
"Ending the idea that ‘the advancement of religion’ is inherently beneficial would make it harder for harmful religious charities to register and easier for the commission to uphold standards consistently," she said.
A commission spokeswoman said: "On 26 April 2019 the commission made an order to disqualify Dr Zakir Naik from trusteeship and holding a senior management function in a charity under section 181A of the Charities Act 2011.
"Dr Naik has challenged the commission’s decision; until this matter is determined by the charity tribunal we are unable to comment further on this issue.
"While it is correct that the commission has not opened a statutory inquiry, as confirmed in our FOI response, we have looked into complaints that have been raised with us. As this is ongoing, we will not comment further on this at this time."
The charity did not respond to inquiries by Third Sector.