Manning was convicted of stealing 750,000 pages of documents and videos before leaking them to WikiLeaks.
Manning, a transgender woman, requested to transfer to a civilian prison after being sent to Fort Leavenworth, an all-male Army prison in eastern Kansas. She was sentenced in 2013 to a 35-year term.
A White House statement on Tuesday said her prison sentence is set to end on May 17.
Obama's decision drew sharp criticism from some Republicans and the President overruled his secretary of defense, who opposed the move.
"All I'll say about the Manning case is I did not support the direction the President went. But he's made his decision," Carter told CNN's Chris Cuomo in an interview that aired Thursday on "New Day." "That was not my recommendation."
A former intelligence official told CNN that the "entire intelligence community is deflated by this inexplicable use of executive power."
The official added that the move was "deeply hypocritical given Obama's denunciation of WikiLeaks' role in the hacking of the (Democratic National Committee)."
Obama spoke about the commutation at his final White House press conference on Wednesday.
"Chelsea Manning has served a tough prison sentence," Obama said. "The notion that the average person who was thinking about disclosing vital classified information would think that it goes unpunished -- I don't think would get that impression from the sentence that Chelsea Manning has served."
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