Singh admitted in a January Sports Illustrated article he had used the spray -- which contains small amounts of IGF-1, a growth factor banned by the World Anti-Doping Agency -- but contended he didn't know the product contained any banned substances.
The tour warned players about deer antler spray in August 2011.
Finchem said Singh had been sanctioned for making the admission, and Singh kept playing while he appealed.
The WADA issued a statement Tuesday indicating the use of deer antler spray is not considered prohibited, because the amount of growth hormone contained in it is too small to trigger a positive test.
Thus, Finchem said, Singh would not face suspension from the PGA and Champions tours.
"Mr. Singh should have contacted the PGA Tour Anti-Doping Program Administrator or other resources readily available to players," Finchem said, "in order to verify that the product Mr. Singh was about to utilize did not contain any prohibited substances, especially in light of the warning issued in August 2011 in relation to deer antler spray."