The motive in this case is unclear, but Vladimir Markin, a spokesman for Russia's Investigative Committee, said both leaders were known for fighting extremism and their professional activity was being investigated as one of the reasons for the attacks.
Mr Yakupov is reported to have been shot as he left his home but managed to reach his car before he died.
He was the head of education at the Spiritual Board of Muslims of Tatarstan.
Interfax news agency reported that he founded Russia's first Islamic literary publishing house and was known as a fierce opponent of Islamic radicalism.
Mr Fayzov, too, was known for his criticism of radical Islamist groups, Russian reports said.
Islamists have carried out a violent campaign against Russian authorities, declaring their intention to establish an Islamic caliphate.
But their activities have been mostly contained to the Muslim republics of Chechnya, Dagestan and Ingushetia in the North Caucasus.
Tatarstan has been much more peaceful and is often held up as an example of religious tolerance in Russia.