Khadija Shah, 25, was taken into custody in May after heroin with a UK street value of about Â£3.2m was found in several suitcases she was carrying.
Her lawyers say Miss Shah's two-month-old daughter Malaika could suffer from unsanitary conditions in jail.
Jail officials have previously said Ms Shah was being treated well.
Miss Shah's lawyer Shahzad Akbar said Malaika had received no immunisations since she was born and said measles and tuberculosis had been detected in the maximum security prison.
He said the baby had been suffering from diarrhoea and had been treated with painkillers that were unsuitable for a baby.
Mr Akbar said: "We are very much afraid she could die."
The court in Rawalpindi heard that Miss Shah, who was heavily pregnant when she was arrested, was accused of trying to smuggle 63kg of heroin from Pakistan to the UK.
If convicted, she could face the death penalty.
Miss Shah argues she was carrying the cases, which the drugs were found in, for someone else and did not know what was in them.
A Birmingham woman arrested in Pakistan on suspicion of trying to smuggle heroin has appeared in court holding her baby, who is also in jail with her.