Players from the countries have been banned by the All England Lawn Tennis Club from all UK grass-court events after the Russian invasion of Ukraine.
However, events outside Wimbledon, such as Queen's and Eastbourne, will retain their ranking points.
"It is with great regret and reluctance that we see no option," said the ATP.
The WTA said it was a "difficult decision".
The International Tennis Federation (ITF) will not grant ranking points in the junior and wheelchair events at Wimbledon, which starts on 27 June.
"The stance we are taking is about protecting the equal opportunities that WTA players should have to compete as individuals," added the WTA, the women's governing body.
"If we do not take this stance, then we abandon our fundamental principle and allow the WTA to become an example to support discrimination based on nationality at other events and in other regions around the world."
In a statement, the All England Lawn Tennis Club expressed its "deep disappointment" and said it was considering its options.
It added: "We believe these decisions to be disproportionate in the context of the exceptional and extreme circumstances of this situation and the position we found ourselves in.
"We remain unwilling to accept success or participation at Wimbledon being used to benefit the propaganda machine of the Russian regime, which, through its closely controlled state media, has an acknowledged history of using sporting success to support a triumphant narrative to the Russian people."
The ATP decision means Serbia's Novak Djokovic - the defending men's champion - will lose his status as the world number one.
Djokovic, a six-time champion at the All England Club, will be unable to retain the 2,000 ranking points he earned by winning the title last year and is only 680 ahead of nearest rival Daniil Medvedev.
Announcing the move, the ATP said: "Unilateral decisions of this nature [by Wimbledon], if unaddressed, set a damaging precedent for the rest of the tour.
"Discrimination by individual tournaments is simply not viable on a tour that operates in more than 30 countries."
It added: "We remain hopeful of further discussions with Wimbledon leading to an acceptable outcome for all concerned."
UK Culture Secretary Nadine Dorries wrote to ATP and WTA bosses earlier this week urging them not to "penalise the AELTC" and said it would send a "completely wrong message to both Putin and the people of Ukraine".
Wimbledon bosses consulted with the UK government before announcing the decision to ban players. Russia was previously banned from defending its Davis Cup and Billie Jean King Cup team titles after the country's invasion of Ukraine - a war supported by Belarus.
The ATP and the WTA have suspended their combined event scheduled to take place in Moscow in October.
The ITF has also cancelled its events in the country.