The Uruguayan striker could also face disciplinary action from the Dutch Football Association who said on Monday it would investigate the incident which was missed by the match referee.
Ajax said on their official website that Suarez would pay an undisclosed fine which will be donated to charity.
Suarez, who has scored seven league goals this season, will miss league matches against VVV Venlo and NEC Nijmegen but he will be available for Tuesday's Champions League match against Real Madrid.
Suarez earned Uruguay a place in this year's World Cup semi-finals when his deliberate handball in the final minute of extra time against Ghana prevented a decisive goal from Dominic Adiyiah.
The striker, who blocked Adiyiah's attempt with two hands on the line, was sent off but his team mates went on to win a penalty shootout.
The incident happened in stoppage time against PSV after referee Bjorn Kuipers showed Ajax's Rasmus Lindgren a straight red card for a rough tackle on PSV playmaker Ibrahim Afellay.
Suarez argued with Bakkal, who stood on the Uruguayan's foot, prompting him to bite Bakkal's shoulder.
"I don't know if he bit hard but this morning I spoke about it with Luis (Suarez)," coach Martin Jol said hours before the club announced the suspension.
"The outcome of our conversation we will announce after the match against Real Madrid, but he will be our captain against the Spaniards," he added.
In 2007, Frenchman Sebastian Sansoni of Vitesse Arnhem bit NEC Nijmegen's Roy Beerens on the nose and received a five-match ban.