He has previously played with the Toronto Maple Leafs and Vancouver Canucks of the NHL and Avangard Omsk of the Kontinental Hockey League.

[5] On 6 May 2019, Mikheyev signed a one-year, entry-level contract with the Toronto Maple Leafs of the National Hockey League (NHL).

[4] On 2 October 2019, during the Maple Leafs' home opener, Mikheyev scored his first NHL goal and added an assist in a 5–3 victory over the Ottawa Senators.

[9] Leafs general manager Kyle Dubas and assistant athletic trainer Jon Geller cleared their schedules so Mikheyev would have familiar people around in the three days between his surgery and flying back to Toronto.

[11] On 20 October 2020, Mikheyev signed a 2-year, $3.29 million contract with the Maple Leafs, avoiding his salary arbitration hearing which had been set for the following day.

[14] It was reported he requested a trade following the season due to a lack of playing time and usage but was denied by Leafs management.

[16] On 13 July 2022, Mikheyev left the Maple Leafs in free agency and signed a four-year, $19 million contract with the Vancouver Canucks.

[16] In his first pre-season game with the Canucks on 25 September during the 2022 training camp, Mikheyev tore his anterior cruciate ligament.

He missed the rest of pre-season and made his debut during the Canucks fourth game of the year against the Columbus Blue Jackets on 18 October.