Vesey notched an assist in Wednesday's 4-3 loss to the Hurricanes.
Vesey scored a goal on three shots and added three hits in Thursday's 3-2 win over the Sharks.
Vesey scored a goal on two shots in Saturday's 4-0 win over the Red Wings.
Vesey (lower body) was activated from long-term injured reserve Saturday, according to Dan Rosen of NHL.com.
Per Vince Z. Mercogliano of USA Today, Vesey (lower body) is practicing Thursday for the first time since he was injured early in training camp.
Vesey (lower body) skated on his own Friday morning, Vince Z. Mercogliano of USA Today reports.
Vesey (lower body) will be placed on long-term injured reserve by the Rangers on Monday, Arthur Staple of The Athletic reports.
Vesey (lower body) will be out of action for a few weeks, according to Vince Z. Mercogliano of USA Today on Monday.
Vesey is being evaluated for a lower-body injury, Vince Z. Mercogliano of USA Today reports.
Vesey is expected to be ready to start the season after experiencing a separated shoulder during New York's postseason run, according to Peter Baugh of The Athletic on Tuesday.