Luthra tweeted a statement on Friday morning in which he expressed his disagreement with the way SportScotland - the body that oversaw his appointment as chair - was looking to run cricket, claiming it was bowing to "the demands of a lobby group and a handful of individuals associated with them - even if that means the wider sport and community will be negatively impacted".
Cricket Scotland was placed into special measures last year after the Changing the Boundaries report found 448 examples of institutional racism in the game.
Luthra said in a six-month update earlier in March that progress had been made on diversity, only for his comments to be criticised by anti-racism organisation Running out Racism. According to the BBC, four members of Cricket Scotland's equality and anti-racism working group subsequently resigned in protest.
"Cricket Scotland can announce that Anjan Luthra has resigned as chair with immediate effect," the board said in a statement. "The organisation thanks Anjan for his hard work and input during his time as chair."
As well as lacking a chair, Cricket Scotland is also currently without a chief executive, after it was announced that interim CEO Gordon Arthur would be stepping down for personal reasons at the end of April.