Meanwhile, the rest of the Sri Lankan team members were fined 40 per cent of their match fees, the ICC said in a release.
Match Referee David Boon imposed the suspension on Sri Lanka after they were ruled to be three overs short of their target at the end of the match.
The decision means Mathews will not be playing in the first two One-dayers of the five-match ODI home series against South Africa on July 20 and 23, respectively, at R Premadasa Stadium in Colombo.
According to the ICC Code of Conduct, which deals with serious over-rate offences, the captain receives two suspension points while the players are fined 10-per-cent of their match fees for each of the first two overs short and 20-per-cent for every additional over their side fails to bowl in the allotted time.
Two suspension points in the Code equates to a suspension from one Test or two ODIs, to be applied to the subsequent international matches.