The 30-year-old Serb was forced to retire from his Wimbledon quarterfinal against Tomas Berdych earlier this month because of the same problem.
The former world No.1 retired hurt during the quarterfinals at Wimbledon
"I feel like I know what it must have been like to watch Picasso."
Qatar booked their berth with a 2-0 victory against Malaysia in their final group match.
The ITF described Nastase's comment about Williams as "highly inappropriate and racially insensitive".
Earlier, Qatar began their campaign with a 2-1 victory over UAE on Monday.
The Qatar Total Open champion becomes number one without ever having lifted one of the four majors in tennis.
He won a record eighth title at the All England Club on Sunday
At 35, the Swiss is Wimbledon’s oldest men’s winner of the modern era
The Spaniard beat five-times champion Venus Williams in straight sets on Saturday
He admits it will be a nice change to see a fresh face on the other side
Makarova, Vesnina in women's doubles title rout
She won 7-5, 6-0 with a supreme display of power hitting in 77 minutes
Victory over Croatian giant Marin Cilic will give Federer a 19th career Grand Slam title.
The Swiss superstar is the second oldest man to make the Wimbledon final, after 39-year-old Ken Rosewall finished runner-up in 1974.