The incident took place during their Rogers Cup tie earlier this month.
An ATP review found the 20-year-old guilty of "aggravated behaviour".
The Australian had already received a $10,000 (£6,400) tournament fine for the "unacceptable comments", which were picked up by on-court microphones.
Although Kyrgios apologised after that punishment, Switzerland's French Open champion Wawrinka, 30, called for major action to be taken.
The fine and suspension will be withheld if Kyrgios does not incur any fines for verbal or physical abuse over the next six months, or accumulate fines totalling more than $5,000 (£3,200) for any other offences at ATP-sanctioned tournaments.
World number 41 Kyrgios also received a $2,500 (£1,600) fine for unsportsmanlike conduct related to a comment made to a ball person during the Rogers Cup match in Montreal.
