Gaurav Endlay pleaded guilty in the Launceston Magistrates Court on Monday to the single charge, which arose during police investigations into the death of baby Charlotte Lukendlay in February, 2016.

There are no current criminal charges in relation to the death of Charlotte, which was the focus of a recent coronial inquest.

The court heard Endlay was holding Charlotte while he argued with his wife Rongrong (Angel) Lu in their Newnham home on either January 14 or 15, 2016.

Endlay's parents were also present, staying with the family while visiting from India.

Endlay struck Ms Lu to the face, causing her glasses to break and her to fall to the floor bleeding from a cut under her eye.

The assault was not reported to the police at the time, and Endlay's father provided first aid so Ms Lu would not need to go to the hospital.

Charlotte was airlifted to the Royal Hobart Hospital on February 21 after she was found unresponsive, and died four days later.

Ms Lu was interviewed by police at the time and said her facial injuries were a result of "tripping over", but then provided a further statement saying Endlay had punched her to the face. She told police she was initially too scared to provide an accurate statement as Endlay had allegedly threatened to kill her and their baby in the past.

In a police interview, Endlay denied striking Ms Lu and said he was not in the room at the time. Police questioned discrepancies in their accounts so, in a subsequent interview, Endlay admitted he pushed Ms Lu away and she fell, hitting her face on the bed.

Endlay spent 18 months in custody before a charge of ill treatment of a child was dropped, the court was told.

Defence counsel Mark Doyle said Endlay accepted that he had committed some form of assault on Ms Lu and her injuries were the result of force, which he described as "spur of the moment".

Mr Doyle said the court could take into account Endlay's time in custody and his limited financial means as a result of his struggles to find work.

"He has suffered the effect of public humiliation and his reputation has been tarnished... irreparably as a result of the allegations that were ultimately not proceeded with," he said.

Magistrate Simon Brown said family violence was "utterly unacceptable" and Endlay should have walked away from the situation rather than striking out.

He accepted that the time in custody was "devastating" to Endlay "personally and professionally".