Umpires inspected the ground in the morning before calling-off the day's play due to rain and wet outfield.
"The match is a draw and man of the match was not awarded to any player," the Orissa Cricket Association (OCA) said.
Rain played spoilsport since day one of the tie as only 33.1 overs of play was possible in the four-day match with the loss of full two days play on the second and fourth day without a ball being bowled.
Tamil Nadu, last year's runner-up, had scored 67 runs in 33.1 over losing three wickets.
On the opening day, only 31 overs of play was possible due to delayed start and the visitors had garnered 66 for two on a seaming pitch with opener Murli Vijay and S Badrinath getting out cheaply.
The second day's play was called off, while only 2.1 overs could be bowled on the penultimate day during which Tamil Nadu lost the other opener in Abhinab Mukund, who departed without any addition to his overnight score of 21.
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For the hosts, Alok Mangaraj accounted for the wickets of Tamil Nadu openers off his 11 overs giving away 21 runs while Basanta Mohanty had scalped the wicket of S Badrinath off his 13.1 overs at the expense of 27 runs.
Odisha will play their next match against Delhi from November 9-12 in New Delhi.