She met members of the Ahmadiyya Mosque in the city’s Kelvingrove area and stressed that Scotland is an inclusive country which celebrates differences.
She first met leaders at the mosque before visiting an area reserved for female members, where she removed her shoes.
She emerged from the visit wearing a pink headscarf before talking with a group of 15 mosque leaders including Rafiq Hayat, UK president of the Ahmadiyya Muslim Community.
The event also marked the launch of a True Islam campaign to promote understanding of Ahmadiyya Muslim beliefs, which differ from those held by most Muslims.
Ms Sturgeon said: “The Scottish Government wants to stand shoulder-to-shoulder with the Ahmadiyya Muslim Community and promote the message that Scotland as a country welcomes diversity.
“We’ve all got a part to play in promoting tolerance and that is challenging extremism.
“I believe that diversity is not a weakness, it’s a strength and it’s something which we should celebrate.”
Ibrahim Ikhlaf, national director of the outreach department of Ahmadiyya Muslim Community UK, said the campaign aims to dispel misconceptions about their religion.
He said: “We want to promote peace, tolerance and harmony in our community.”
Mr Shah was found seriously injured outside his shop in the Shawlands area of Glasgow on March 24 and was pronounced dead in hospital.
He had moved from Pakistan to Glasgow almost 20 years previously, and was attacked because his 32-year-old killer Tanveer Ahmed believed he had ‘’disrespected the Prophet Muhammad’’.
After visiting the mosque, Ms Sturgeon spoke at a Peace Symposium at Glasgow University.
She said the Ahmadiyya community’s campaign demonstrates its commitment to promoting peace, tolerance and understanding.
Ms Sturgeon added: “There is no doubt that this kind of engagement and outreach work is vital to tackling the root causes of prejudice and hatred and create the inclusive, tolerant and cohesive Scotland we all want to see.”
The Shah family had moved to Scotland from Pakistan in the 1990s to escape persecution as a result of their religious beliefs.
Ahmed, a father-of-three from Bradford who did not know Mr Shah, claimed to have been offended by clips the shopkeeper had posted online which he said ‘’disrespected the Prophet Muhammad’’.
Ahmed was given a life sentence at the High Court in Glasgow after admitting murder.