There are fears that the soldier's extraordinary actions may have compromised his personal security because photographs and videos of him pulling civilians to safety have been published and broadcast around the world.
He wore a balaclava as he fought the al-Shabaab terrorists in a gun battle.
On Thursday police in Kenya arrested the wife and mother of one of the jihadists as they launched a manhunt for the mastermind behind the attack.
Investigators said they had been able to identify one of the five gunmen involved in the assault through a mobile telephone left on his corpse.
They named him as Ali Salim Gichunge. Police said they had detained his wife Violet after discovering that she had posted an advertisement on Facebook attempting to sell many of their household goods the day before Tuesday’s attack.
“We are moving out of Nairobi this week so it is a quick sale,” she wrote. “Prices slightly negotiable.”
Neighbours described the couple, who moved to the outskirts of Nairobi in October, as quiet and fond of cats, local newspapers reported. Police said they had arrested a total of 11 people, including Ms Gichunge’s mother Mariam.
The Somali militant group Al-Shabaab, which has pledged allegiance to al-Qaeda and adheres to a violent and rigid interpretation of Islam, on Wednesday claimed responsibility for the assault.