While Owaisi is out of the country, according to sources in his party, Reddy is undergoing treatment at a hospital here.
TRS president and Chief Minister K Chandrasekhar Rao spoke to Reddy's family members and told them that Reddy need not come for voting in view of his health, a release from his office said.
Rao was the first to cast his vote in the Assembly.
The TRS had earlier declared support to NDA nominee Ram Nath Kovind in the election.
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The party yesterday conducted a meeting of its MLAs to familiarise them with the voting procedure.
The value of each MLA's vote in Telangana is 132.
The authorities had made elaborate arrangements for the election.
Kovind, and Meira Kumar, the former Lok Sabha Speaker who is the UPA nominee for the presidential poll, had earlier visited Hyderabad to mobilise support for their candidature.
Kovind is assured of the support of NDA partners BJP and TDP.
In the 119-member Telangana House, excluding a nominated member who doesn't have the right to vote in the presidential election, the ruling TRS has 82 members, the Congress (19), MIM (7), BJP (5), TDP (3), CPI (1), CPI-M (1) and Independent (1).
There are 17 Lok Sabha members and 10 Rajya Sabha members from Telangana.
Noting that Kumar was the Lok Sabha speaker when the Andhra Pradesh Reorganisation Bill (for the formation of Telangana) was passed, the Congress had earlier said all electors in Telangana should vote for her as an expression of gratitude.
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