The meeting lasted about 25 minutes and there was no official word on the delberations.
R Radhakrishnan, MP, and AINRC MLA V Bhalan were among those present during the meeting, party sources said.
Shah was here on a day's visit to participate in party sponsored functions, including a workers meeting.
BJP is an alliance partner of the ruling AINRC and has a nominated legislator in the Assembly.
AINRC's Radhakrishnan won as the NDA candidate in last year Lok Sabha polls, defeating Congress candidate and former union minister V Narayanasamy by a margin of more than 60,000 votes.