Heijblok started his career at amateur side Hollandia before signing his first professional contract at HFC Haarlem in 2003 where he became their first goalkeeper straight away. In four seasons he had 126 appearances for the club, all at Eerste Divisie level. He then signed for Eredivisie side Ajax where he became their third goalkeeper behind Maarten Stekelenburg and Dennis Gentenaar for the 2007–08 season.
After Ajax, Heijblok signed for Eredivisie-side De Graafschap on June 30, 2008. After one season he then transferred to 2008–09 Eredivisie champions AZ Alkmaar on June 24, 2009 for two seasons.