Alexander Kanishchev began his professional career in the second team of Zenit, Leningrad, when he was 16 years old, not having an opportunity at the time to earn a place in the first team, as most of the young players of that time he went to play in the second soviet league, in the team Karshistroi, Qarshi, Uzbekistan. There he played from 1978 to 1980 with fellow Leningrad players and friends Sergey Vedeneev and Aleksei Stepanov.
In 1980, he became the player of the Leningrad team "Dynamo". There he played almost two years.
In 1982 happened one of the most influential events in his football career. Jānis Skredelis invited him to Daugava Rīga in which Alexander Kanishchev became famous as one of the most technically skilled attacking midfielder in the 1st Soviet league. With Genadi Shitik and Yuri Popkov he formed one of the strongest midfield lines in the 1st Soviet league, and playing together with strikers like Evgenii Milevskii and Aleksandr Starkov in 1985 with Daugava won the first league title. In 1986 Kanishchev was invited by Pavel Sadyrin to come back to Leningrad, USSR, to become the player of Zenit Leningrad. He played in Zenit for two (1986–1987) seasons.
In 1988, he returned to Daugava which by then was also on the fall. Kanishchev in 1990 joined the Ukrainian team Metalist, Kharkiv for a short period. It was the last team in which he played in the Soviet Union.
Over the three seasons that he played in the Soviet Top League, Kanischev played 55 matches and scored 5 goals, in the first league with Daugava he capped 221 appearances and scored 37 goals.
Later he received an invitation from the Polish club "Pogon" from the town Szczecin, located near the border with Germany. There he quickly became one of the leaders, helping the squad to rise to one of the top positions in its 2nd League. Consequently, "Pogon" Szczecin earned the place to play in the highest league of Poland. After successful performance in "Pogon" he was invited to "Legia" Warsaw, which was one of the most famous clubs in Poland. He played there only half a year, when his knee was heavily injured, and after being treated for a long time, decided to finish his career.
After finishing the career, succeeding in business, he created the non-commercial Fund of helping veterans of professional sport "Zenit-84". This organization is formed and shared by the ex-players of the Zenit Leningrad 1984, the squad, which won the USSR highest league championship that particular year, and other veterans of Zenit and local teams of Leningrad (St.-Petersburg).
The fund exists for providing people, involved in it, the opportunity to play veteran tournaments, participate in charitable social and sport events. Traveling around the world, playing with different teams, the veterans Team of Zenit meets incredible amount of fans from USSR (Russia) and all around the globe, still wishing to see the beloved team in action. The main football club FC Zenit Saint Petersburg and its main sponsor Gazprom partly participates in the life of the fund, bringing help for the organization and players themselves, providing some moral and financial support.
Alexander today is the entrepreneur, businessman, the player of veterans team of the Zenit, and the president of the above-mentioned Fund "Zenit 84".