The move by the Togo-based carrier follows the death of one of its passengers from the virus after they had travelled from Liberia to Nigeria via the Togolese capital Lome.
The 40-year-old man, an employee of the Liberian government, died in Lagos on Friday in Nigeria's first confirmed death from Ebola.
"The suspension of flights to Freetown and Monrovia by ASKY is related to the fight against the spread of the Ebola virus," Afoussath Traore, a spokesman for the company, told AFP.
"ASKY took this precautionary measure to ensure the safety of all: its passengers, staff and people of all countries covered by our network," said Traore.
ASKY, which works in partnership with Ethiopian Airlines, serves 20 destinations in central and west Africa.
Since March, there have been 1,201 cases of Ebola and 672 deaths in Guinea, Liberia and Sierra Leone, according to the US Centers for Disease Control and Prevention.
On its website, ASKY also announced that it would stop transporting food from Conakry in Guinea and would screen all passengers travelling from the Guinean capital.
Nigerian carrier Arik also said on Sunday it was halting direct flights to Liberia and Sierra Leone, which have seen close to 350 deaths from Ebola between them.
Ebola can fell victims within days, causing severe fever and muscle pain, vomiting, diarrhoea and, in some cases, organ failure and unstoppable bleeding.
The highly contagious and often fatal disease spreads among humans via bodily fluids, including sweat, meaning one can get sick from touching an infected person.
With no vaccine, patients believed to have caught the virus must be isolated to prevent further contagion.