The sanction - the heaviest imposed on a Premier League manager - was imposed by an independent regulatory commission after Pardew admitted a Football Association misconduct charge.
Pardew was also warned as to his future conduct after the incident during Newcastle's 4-1 win at Hull City on March 1.
The 52-year-old headbutted Meyler on the touchline when the midfielder tried to retrieve the ball from the Newcastle technical area.
A statement from the FA read: "Newcastle United manager Alan Pardew will serve a seven-match suspension with immediate effect, subject to any appeal, after he admitted an FA misconduct charge.
"An independent regulatory commission today ruled the first three matches imposed are a stadium ban with the remaining four a touchline ban."
Newcastle, who have already fined Pardew £100,000 and issued their manager with a formal warning, said they have accepted the decision and now wish to draw a line under the matter.
Pardew told the club's official website: "As I have made clear, I deeply regret the incident and again wholeheartedly apologise to all parties for my conduct, which I understand was not acceptable.
"I will accept the punishment handed down by the FA today.
"My focus now turns to preparing the team for this weekend's game against Fulham and finishing the season as strongly as possible."
Pardew will be suspended for matches against Fulham, Crystal Palace, Everton, Southampton, Manchester United, Stoke, and Swansea - but will be back for the last three games of the season.