In Australia, the AFL has something similar to this called the NAB AFL Rising Star Award (winner gets the Ron Evans medal).

The criteria is as follows from Wikipedia

Every round, an Australian Football League rising star nomination is given to a standout young player who performed well during that particular round. To be eligible to be nominated for the award, a player must be younger than 21 years of age on 1 January of the award year and have played 10 or fewer senior games before the beginning of the season. A player who is suspended1 during the season is not eligible to win the award but is still eligible for nomination

Notes

• Players are generally 18 when they're first drafted into the AFL
• There are 22 regular season games (+ up to 4 finals for a grand finalist) in a season. In the NBA this would mean players can play just under half a professional season by their normally third or fourth professional season to retain eligiblity.

I would imagine that baseball has a similar crtieria method given a player can be classified as a rookie after they've been called up to the majors in a previous season.