The Board of Control for Cricket in India (BCCI) had on Monday written to the CA refusing to play under lights after which the Australian board confirmed playing the Islanders in a day/night game in January.
"We can confirm that we have received advice from the BCCI that it is not prepared to participate in a proposed Day-Night Test in Adelaide this summer," a CA spokesperson was quoted as saying.
"Whilst we appreciate some Adelaide fans may be disappointed, we know how popular the Adelaide Test is and look forward to hosting India there in December.
"We are committed to hosting at least one day-night Test each home summer as part of our continued focus to grow Test cricket, and we are excited about the Day-Night Test against Sri Lanka at the Gabba in January," he added.
According to the current International Cricket Council (ICC) Playing conditions, a home nation can only host a day-night Test match "with the agreement of the visiting board" and India have confirmed that they want the match played with a traditional red ball.
India are one of only two current Test-playing nations to have avoided playing pink-ball cricket at the international level, with Bangladesh the other.
In contrast, Australia have played four pink-ball Tests and won all of them, including the historic first game against New Zealand in Adelaide in 2015.
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