The Scottish First Minister said she is "consumed with sadness" and anger at the death of 34-year-old Mercy Baguma.
The Ugandan woman's body was discovered by police in Govan on Saturday.
The Positive Action in Housing (PAIH) charity said Ms Baguma's one-year-old son was "found crying beside his mother’s body, weakened from several days of starvation".
The baby has since been released from hospital into the care of his father.
Speaking at First Minister's Questions, Ms Sturgeon said: "I find myself consumed with sadness but also with real anger at the death of Mercy Baguma."
Ms Sturgeon continued: "We knew this before this tragedy, but it is underlined by this tragedy – the UK asylum system is not just broken, it is deeply inhumane and it must be changed.
"People who come to Scotland because they need a place of safety should have our support, and that is even more true right now at this time of crisis."
Ms Sturgeon said her government has repeatedly raised concerns about the Westminster-reserved asylum process.
She added: "We need wholesale reform of our asylum system and we need to start from the principle of dignity, of empathy and of support for our fellow human beings who come to this country, seeking support at desperate and dismal times of their lives.
"I would appeal to the UK government to look into their hearts as a result of this case and finally make the changes that are needed to housing."
Ms Sturgeon added she would support all efforts to investigate Ms Baguma’s death, including backing the PAIH charity’s calls for an inquiry into the accommodation situation faced by asylum seekers in Glasgow during the coronavirus pandemic.
Positive Action in Housing has previously warned about the asylum seeker "accommodation crisis" in Glasgow, in the wake of an attack carried out in the city in June.
The Crown Office has said the Procurator Fiscal has received a report in connection with the Ms Baguma's death and an investigation is under way.