Misbah pleaded guilty to a "serious over-rate offence" after his side fell three overs short of completing their target in the required time, as Sri Lanka won by two runs.
The suspension means Misbah will miss the chance to break the Pakistan record for most consecutive Tests as skipper, which stands at 15.
The International Cricket Council confirmed Misbah's ban, with his team-mates also docked 40% of their match fee, despite it being their first serious over-rate offence in the past year.
"As this was Pakistan's first serious over-rate offence in the past 12 months, Chris Broad of the Emirates Elite Panel of ICC Match Referees handed Misbah two suspension points while each of his players received a 40% fine (10% for each of the first two overs and 20% for the additional over)," the ICC said in a statement.
"The imposition of two suspension points means that Misbah will now miss Pakistan's first Test against Sri Lanka which starts in Galle from Friday, since such suspension points are to be applied to the subsequent international matches in which Misbah is most likely to participate on a chronological basis immediately following the announcement of the decision."
The first of the three-Test series begins in Galle on Friday.