Budaj will call it a career following the end of AHL Ontario's 2018-19 campaign.
Budaj was demoted to AHL Ontario on Tuesday, per the AHL transactions page.
Budaj stopped 2-of-3 shots in relief during Wednesday's 7-3 loss to the Avalanche.
Budaj (illness) will serve as the backup goalie for Friday's game versus the Blackhawks, Curtis Zupke of the Los Angeles Times reports.
Budaj is under the weather and could miss Friday's clash with Chicago, Jon Rosen of Fox Sports West reports.
Budaj will start Tuesday's game versus the Maple Leafs, Lance Hornby of The Toronto Sun reports.
Budaj was officially assigned to AHL Ontario on Monday after clearing waivers, Jon Rosen of Fox Sports West reports
Budaj was placed on waiver by the Kings on Sunday, TSN reports.
Budaj allowed two third-period goals against Vancouver, stopping seven of nine shots overall and leading to a 4-3 overtime loss Thursday.
Budaj is projected to cover the road net against the Canucks on Thursday night, Jon Rosen of Fox Sports West reports.