The story, which was broadcast last week, said Mr Trump called Mr Magufuli an "African hero" compared to other leaders who are "doing nothing".
A statement from TBC said editorial procedures had not been followed.
The broadcaster's Director General Ayub Chacha said that the station should have verified the information before broadcasting.
The story said that the US president had called on other African leaders to follow Mr Magufuli's example with his emphasis on good governance and his war against corruption.
Mr Magufuli, known as the "bulldozer" for his hands on approach to leadership, has been waging a public war on corruption which has won him some support locally and internationally.
The article said that Mr Trump made the comments while signing an executive order excluding Tanzanians from the ban on some people entering the US.
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