They were called up from the club's AHL affiliate in Syracuse.
Foote and Leclaire sustained undisclosed lower-body injuries in Sunday night's 6-2 victory over Ottawa. Fredrik Norrena will take over as the Blue Jackets' No. 1 goaltender.
Novak, 24, has played one game for Columbus and 22 for Syracuse this season. The native of Czech Republic was the New York Rangers' first-round pick in the 2000 NHL Entry Draft. In 12 career NHL games, including 11 with Ottawa in 2005-06, he has yet to score.
Conklin, 30, has a 2-10-1 record with a 3.33 goals-against average in 14 games with Syracuse this season. He was signed as a free agent with the Blue Jackets in July after spending five seasons in the Edmonton Oilers organization. In 60 career NHL games, he has a 27-19-5 record with a 2.49 goals-against average.