Beleskey was sent down to AHL Hartford on Sunday.
Beleskey (shoulder) is considered day-to-day, Rick Carpiniello of The Athletic reports, which means he could be available Tuesday against Florida.
Beleskey (shoulder) was placed on injured reserve retroactive to Sept. 24, per the NHL's official media site.
Beleskey is expected to miss 2-4 weeks due to a separated shoulder, Stephen Whyno of the Associated Press reports.
Belesky injured his shoulder and will not return to Monday's preseason contest against New Jersey.
While it originally appeared Beleskey would start off with the Rangers, he's in the lineup for AHL Hartford on Sunday, Mark Divver of The Providence Journal reports.
Beleskey was recalled from AHL Hartford on Sunday after being traded to the Rangers, per the AHL's official transaction log.
The Rangers acquired Beleskey, defenseman Ryan Lindgren, forward Ryan Spooner and a 2019 seventh-round pick from the Rangers on Sunday in exchange for forward Rick Nash.
Beleskey took a puck to the face during a 3-2 defeat to AHL Bridgeport on Friday, and suffered a broken orbital bone from the incident Mark Divver of The Providence Journal reports.
The Bruins have placed Beleskey on waivers, the Boston Herald reports.