Moe began his career playing for the Atlantic City Sea Gulls in the Eastern Amateur Hockey League (EAHL).

[2] In the off-season he was named to the AHL First All-Star Team,[3] and his rights were traded to the National Hockey League's New York Rangers.

[4] Midway through the following season Moe was accused of delivering an illegal low hit to the Chicago Black Hawks' Bill Mosienko which resulted in a torn knee ligament.

[2][6] In his NHL playoff debut, on March 24, 1948 against the Detroit Red Wings, Moe fractured two vertebrae after throwing a check at Bill Quackenbush.

[2] Prior to the start of the next season Moe was involved in an automobile accident with four of his teammates, as they were retiring from exhibition games in Quebec.

[2] During the off-season the Rangers traded Moe, along with the rights to Lorne Ferguson and future considerations to the Bruins for Pat Egan and cash.

After his two seasons in Hershey, Moe moved to the Pacific Coast Hockey League playing for the Calgary Stampeders.