Spectators at the DC Open were warned that Ukraine's Elina Svitolina would not shake hands with Victoria Azarenka.
Belarusian Azarenka was booed after Svitolina beat her at Wimbledon and to avoid a repeat, the scoreboard showed a message during Svitolina's 7-6 (7-2) 6-4 first-round win in Washington DC.
"It's the right thing," said world number 27 Svitolina.
"I asked for the WTA [Women's Tennis Association] to respect the decision of Ukrainians and they did."
At the end of the match, both players headed straight to the sidelines and the umpire.
Two-time Australian Open champion Azarenka, playing on her 34th birthday, said the warning to fans had arrived "18 months too late" and asked whether it was a big story.