"This decision has been driven by our commitment to deliver the best possible outcomes for our loyal audiences and the best possible experience for our own people", he said.
In a statement Guthrie has said she is "devastated" by the decision "despite no claim of wrongdoing" on her part and is considering her legal options.
"As the first female managing director of the ABC, I felt a tremendous responsibility and unique privilege to lead Australia's most important cultural institution", she says.
Morrison said it wasn't his place to comment on the efficacy of Guthrie as managing director, again pointing to the board as the folks in charge of that call.
In June, high-profile Melbourne ABC mornings presenter Jon Faine slammed her at the Melbourne Press Club for her "failed strategy" and "staying silent" after the former Turnbull government freezed its funding by $84 million over three years in the May budget.
"I am considering my legal options", Guthrie said.
"I personally think Michelle has done a good job and the board has been very happy with many, numerous things that she does".
She stepped down in March this year to focus on her role at the ABC.
Anderson will serve as acting managing director while Guthrie's permanent replacement is found. Anderson is now Director, Entertainment & Specialist and has worked in the media industry for more than 30 years.
The ABC managing director is appointed by the broadcaster's board, independent of government.
He also said the ABC's relationship with the federal government "could have been better" under Ms Guthrie.
"By law, Managing Directors are selected by the ABC Board independently of the Government and Opposition of the day", the ABC noted in its statement.
Sally Neighbour, executive producer of 4 Corners, tweeted: "excellent decision".
The secretary of the ABC section of the Community and Public Sector Union, Sinddy Ealy, said the board had done the right thing.
"The ABC board has legislated independence in relation to management appointments and the Government respects the duty and role of the board in these matters".