2010-11: Dylan Malmquist played bantam hockey in Edina, Minnesota and was invited to USA Hockey's Select 15 Development Camp in July.
2011-12: Malmquist was the second-leading scorer for Edina HS as as a ninth-grader and attended USA Hockey's Select 16 Development Camp. In 30 games he scored 26 goals with 23 assists — including three goals and two assists in three games as the Hornets captured the Section 3AA championship — and had 20 penalty minutes. Edina lost to Benilde-St. Margaret's in the AA state tournament and fell to Duluth East in the consolation tournament. Malmquist was selected by Muskegon in the first round (10th overall) of the 2012 USHL Futures Draft.
2012-13: Malmquist was again Edina's second-leading scorer behind Connor Hurley (BUF) in his sophomore season and skated for Team Southeast in the Upper Midwest Elite HS League in the fall. He scored 24 goals with 22 assists and had 24 penalty minutes in 30 games for Edina as the Hornets won their second straight Section 3AA title and defeated Lakeville North, Duluth East and Hill-Murray to win the 2013 AA state championship. Malmquist scored 6 goals with 8 assists and 14 penalty minutes in 12 games for Team Southeast. He participated in USA Hockey's Select 17 Player Development Camp and was chosen to play for USA's U18 team at the 2013 Ivan Hlinka Memorial Tournament in August.
2013-14: Malmquist skated for the USA in the 2013 Ivan Hlinka Memorial tournament in August and in September committed to playing college hockey at Notre Dame in 2015-16. He skated for Team Southeast in the UMEHSL in the fall before winning his second straight state championship with Edina as a junior. Malmquist was +2 with no points and 2 penalty minutes in five games at the Ivan Hlinka tournament as the USA finished second; falling to Canada 4-0 in the gold medal game. He was Edina's third-leading scorer behind Miguel Fidler and Cullen Munson. The Hornets captured the Section 3AA title and defeated Stillwater, Eagan and Lakeville North, out-scoring the three opponents 17-4 in the state tournament. Malmquist scored 6 goals with 12 assists in 15 games for Team Southeast. He was ranked 182nd amongst North American skaters in Central Scouting's final rankings prior to the 2014 NHL Draft.