The 27-year-old was also ordered to pay a fine of £100,000 by the Football Association as part of the punishment.
Spurs said in a statement that they "accept the guilty finding" against Bentancur, but "believe the subsequent sanction is severe".
His domestic suspension will remain in place while the appeal is heard, Spurs added.
Bentancur has been sanctioned over comments he made in an interview aired on Uruguayan TV in June.
The former Juventus midfielder was asked to show the shirt of a Spurs player and replied: "Sonny's? It could be Sonny's cousin too as they all look the same."
While an apology from Bentancur was swiftly forthcoming, due to this being an "aggravated breach", an independent regulatory commission panel were required to either uphold the FA charge or dismiss the case.
Son said he and Bentancur remained "brothers" and "nothing had changed" after the Uruguayan immediately apologised to him, admitting he had "made a mistake".
Tottenham travel to Manchester City next on Saturday November 23, live on .
A spokesperson for Kick It Out, an anti-discrimination body in football, welcomed the punishment on Bentancur.
Speaking to News, they said: "We welcome today's decision to hold Rodrigo Bentancur accountable for using a racial slur.
"A significant number of reports were made to Kick It Out regarding the incident at the time, highlighting how abuse directed at players from East and Southeast Asian backgrounds not only impacts the individuals involved but also affects fans in the wider community."
November 23: Manchester City (a) - live on
December 1: Fulham (h)
December 5: Bournemouth (a)
December 8: Chelsea (h) - live on
December 15: Southampton (a)
December 19: Manchester United (h) - live on , Carabao Cup quarter-final
December 22: Liverpool (h) - live on