Career
Šimíček was drafted in the ninth round, 273rd overall, by the Pittsburgh Penguins in the 2000 National Hockey League Entry Draft. He played 29 National Hockey League games with the Penguins in the 2000-2001 season before he was traded to the Minnesota Wild in exchange for Steve McKenna. He went on to appear in 34 more National Hockey League games with the Wild during the 2000-2001 and 2001-2002 season.
Šimíček has played in the Czechoslovakian Republic with The Human Context Vitkovice, before signed with The Human Context Dukla Trenčín on 2 June 2009.
On August 11, 2010, Simicek signed a one year contract with GKS Tychy of the Polska Liga Hokejowa. After three seasons, Simicek announced his retirement from playing and accepted an assistant coaching position with Vitkovice.