Justice Manmohan said the Mr Goswami and his channel can put out stories by stating the facts related to the investigation into the death of Sunanda Pushkar, but cannot call the Lok Sabha MP from Thiruvananthapuram a "criminal".
The court also said that just because Mr Tharoor was not coming to their show or not giving an interview, cannot be a reason to say that he was "running away", as was said on the channel.
A person has a "right to be silent", it said with regard to the lack of response from Mr Tharoor and added that "someone has not understood how our law operates".
The observations by the court came as it issued notice to the journalist and his channel seeking their response to Mr Tharoor's plea claiming Rs 2 crore damages from them for allegedly making defamatory remarks against him while airing news relating to the death of his wife.
The court did not pass any interim order blocking the channel from airing its stories, but said "whatever be the provocation, you (Goswami) cannot call him a criminal masquerading as a politician. That is uncalled for and it is presumptive".
"You cannot use language like this. You cannot call him names. Bring down the rhetoric," the court said.
Thereafter, senior advocate Sandeep Sethi, appearing for the journalist and the channel, said he will advise his clients accordingly.
Mr Sethi also said that his clients will place on record the justification for the statements made against Mr Tharoor and therefore, no interim order should be passed.
The court, thereafter, listed the matter for hearing on August 16.
During the arguments, senior advocate Salman Khurshid, appearing for Mr Tharoor, said that since May 6, when the channel was launched, it has been airing 3-5 hours long news shows every day entirely on the case of Sunanda Pushkar's death and making defamatory statements against the MP.
The lawyer said the channel and the journalist have condemned Mr Tharoor as guilty and he should be arrested.
The court said a journalist has a right to investigate which cannot be curbed, but added that it has to be tempered and balanced.
To this, Mr Tharoor's lawyer said that the balance has been "skewed" in this case as the reporting was "one-sided".
The channel on the other hand said that it has only aired facts regarding the investigation.
It told the court that it had reports of senior police officers associated with the probe who have said that evidence was not gathered properly and was allowed to be tampered with.
The channel claimed it also has audio tapes of Sunanda Pushkar's conversation with a reporter just a day prior to her death.
Mr Tharoor's lawyer opposed the contentions saying the police, which was probing the case, had not said anything, but the channel's statements have harmed his reputation apart from causing emotional hurt and pain.
According to Mr Tharoor, Arnab Goswami earlier as the editor-in- chief with another news channel had aired such news, which was restrained by the National Broadcasting Standards Authority.
In the lawsuit, he has claimed to have suffered humiliation and severe loss of reputation in the eyes of the public and "he has baselessly been declared by the defendants as the alleged murderer of his late wife".
Sunanda Pushkar was found dead in a suite of a five-star hotel in South Delhi on the night of January 17, 2014.