Pardew, who has accepted the punishment, has also been fined £60,000 and warned about his future conduct by an independent regulatory commission after admitting a misconduct charge.
It is the longest ban ever handed out to a Premier League manager, and not since Brian Clough was banned from the touchline - from February 1989 until the end of that season for hitting fans who invaded the pitch - has a boss at a league club been given such a stiff punishment.
Pardew, who has also been fined £100,000 and given a formal warning by his club, said he will not appeal against the sanction.
The Newcastle manager said in a statement: "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 banned from Craven Cottage for Newcastle's match at Fulham, and then from St James' Park for the home games against Crystal Palace and Everton.
The touchline bans will kick in for the games against Southampton (away), Manchester United (home), Stoke (away), Swansea (home).
The 52-year-old appeared at a personal hearing in front of a three-man commission. It is believed the panel also looked at recent incidents over the last two seasons.
Pardew was given a two-match touchline ban and £20,000 fine in August 2012 for pushing an assistant referee, and was also warned about his conduct in January this year following a heated exchange when he was caught on camera swearing at Manchester City boss Manuel Pellegrini.
The clash with Irish midfielder Meyler occurred during Newcastle's 4-1 win at Hull on March 1, which led to Pardew being sent to the stands by the referee.
After the commission's hearing, the FA announced the punishment in a statement which 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 [Tuesday 11 March 2014] ruled the first three matches imposed are a stadium ban with the remaining four a touchline ban."