Shah had to postpone his visit following a meeting of NDA chief ministers in Delhi today and his subsequent required presence in various other important meetings, BJP State unit president Tamilisai Sounderrajan said.
As a result, Shah's visit to Tamil Nadu as part of the 95-day nation wide tour has been "postponed", she said in a statement.
The new schedule for his visit would be announced later, she added.
The BJP chief was slated to attend a series of events in Chennai and Coimbatore during his August 22-24 state tour.
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Shah was earlier scheduled to visit Tamil Nadu in May but the trip was postponed.
With an eye on the 2019 Lok Sabha polls, the BJP chief is travelling across the country to strategise and find ways to strengthen the party at the grass-root level.
While BJP has one Lok Sabha MP from Tamil Nadu, it has no representation in the 234-member state Assembly, dominated by the AIADMK.