Miller is the most noteworthy of the two call-ups, considering the 19-year-old winger is regarded as one of the organization's top prospects.
The 2011 first-round draft pick (15th overall), who played for Team USA in the recent World Junior Hockey Championship, has eight goals and 12 assists in 37 games this season for the AHL's Connecticut Whale.
Should Miller dress Tuesday against the Devils, he will make his NHL debut. The Rangers then will have five games in which to assess whether to return him to the AHL or keep him with the big club while burning a year of eligibility on his entry-level deal.
Mashinter, 23, has three goals and four assists in eight games for the Whale since being acquired in a trade with San Jose earlier this season.
To make room for Miller and Mashinter's arrival, Benn Ferriero was reassigned to Connecticut after spending four games with the Rangers.