Diana Sacayan, a well-known activist for lesbian, gay, bisexual and transgender (LGBT) rights, was found dead in Buenos Aires on Tuesday.
It is the third violent transgender death in the country in the past month.
Latin America accounts for most transgender murders worldwide, rights groups say.
Rights group Amnesty International said on Wednesday that the body of Ms Sacayan, discovered in her flat, showed signs of violence.
"A dark cloud has set over Argentina's trans community," said Mariela Belski, Executive Director of Amnesty International Argentina.
"Unless this latest wave of murders is effectively investigated and those responsible taken to justice, a message will be sent that attacking trans women is actually ok."
President Fernandez echoed Amnesty's concerns.
"I ask the national security services and the metropolitan police to solve this horrible crime," she said during a public address.
Ms Sacayan, 40, had been the leader of a number of organisations seeking equality for Argentina's LGBT community.
In 2012 she was personally given her national identity card by President Fernandez, recognising her as a woman - a first for Argentina.
Ms Sacayan's death followed the killings of Marcela Chocobar and Coty Olmos, two transgender women whose bodies were found over the last month in the provinces of Santa Fe and Santa Cruz.
Latin America accounted for 78% of the 1,731 murders of transgender and gender-diverse people reported worldwide between January 2008 and December 2014, according to activist group Transgender Europe.

Daron Dylon Wint, 34, who had previously worked for the victims' family business, was detained late Thursday in the US capital.
He is accused of killing the four victims and setting the house on fire.
Police refused to confirm reports Mr Wint was identified by DNA from the crust of a pizza delivered to the home.
Savvas Savopoulos, 46, chief executive of American Iron Works, was found dead in his family's home in Woodley Park, northwest Washington, just blocks away from the home of Vice-President Joe Biden.
Police discovered his body alongside those of his wife Amy, 47, his 10-year-old son Philip and housekeeper Veralicia Figueroa, an El Salvador national.
A week after the gruesome discovery, investigators have provided few details in a case that has shocked the city and its high-profile social circles.
There have been media reports of a $40,000 cash drop being made to the home hours before the incident, and a text message from Mrs Savopoulos telling a member of staff not to come into work that same day.
The Washington Post reported that a delivery order was placed with a local pizza company while the family was being held hostage and DNA found on a crust has been matched to Mr Wint.
Police officials would not confirm or deny this report to the BBC.
Argentine President Cristina Fernandez and Amnesty International have called for justice after the violent death of a transgender activist.
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Police have arrested a man they believe held a family and housekeeper hostage in their Washington DC home before killing them.