Smith will miss at least 24 days or 10 games after being placed on LTIR. He was absent at practice Friday and did not play in the second half of the team's back-to-back against the Vancouver Canucks.
The Oilers recalled goaltender Stuart Skinner from their taxi squad on an emergency basis on Jan. 14. Rodrigue is expected to join Edmonton's taxi squad from the Austrian League once he completes the NHL's COVID-19 protocols.
Smith returned to the Oilers on a one-year $2 million deal. The 38-year-old appeared in 39 games for Edmonton in 2019-20, winning 19 of his 37 starts and had a .902 save percentage and 2.95 goals-against average