The ban is the third time that Hill has fallen foul of the NFL's strict rules on substance abuse, having also been banned in October 2012 and for four games of last season.
The third strike could have brought about a season-long suspension for Hill, similar to the one meted out to Arizona Cardinals safety Daryl Washington today, but the league has chosen to limit the ban to six games.
The 24-year-old had initially appealed the NFL's findings, but that was turned down and he will now not be eligible for the active roster until October 13.
That means that he will miss matches against the Detroit Lions, Arizona Cardinals, Houston Texans, Washington Redskins, Atlanta Falcons and Philadelphia Eagles.
However, the former undrafted rookie is free to take part in OTAs, training camp and pre-season matches for the Giants.