The club also said right-winger Anson Carter will miss up to two weeks with a sprained shoulder.
Leclaire injured his hamstring on Dec. 22 against Vancouver and will be sidelined indefinitely. He had appeared in 21 games with the Blue Jackets this season and has a 6-12-2 record with a 2.97 goals-against average.
Conklin stopped 10 of 11 shots in two games with the Blue Jackets this season, relieving Fredrik Norrena on Dec. 16 against Chicago and again on Dec. 20 at Detroit. He is 2-10-1 with Syracuse this year. He spent the past five seasons in the Edmonton Oilers organization, posting a 27-19-5 record in 62 NHL games and signed with the Blue Jackets as a free agent last summer.
Lindstrom has two goals and six assists in 14 games with Syracuse this season. The team's second pick in the 2002 draft made his NHL debut with the Blue Jackets last season and was scoreless in three games.