The cancer was discovered in November last year. Navratilova was previously diagnosed with breast cancer in 2010 and recovered.
Martina said her prognosis is good and she will start treatment this month.
In a tweet, former world No. 1 Navratilova called the decision "pathetic".
The tennis legend has been a vocal critic of Indian Prime Minister Narendra Modi.
The Serbian struck a line judge with a ball following a point during the first set of his match against Spain's Pablo Carreno Busta on Sunday.
Court, who holds the all-time record of 24 Grand Slam singles titles, has been heavily criticised for voicing her religious-based opposition to same-sex marriage and transgender athletes.