The attack took place in a busy street on Tuesday evening, the San Francisco Police Department said on Wednesday.
The attacker used a large military-style knife in an unprovoked assault, authorities said.
Both women were senior citizens, with Chui Fong Eng aged 85 and the other woman, who has not been named, aged 63.
They have been hospitalised with multiple stab wounds, however both were said to be out of danger.
The injuries sustained by the two women were believed to be life threatening at the time of attack.
“I was told the knife nicked her lung and ribcage. It was a really long knife,” Ms Fong’s grandson, Drew Eng, told ABC TV.
The alleged attacker was identified as 54-year-old Patrick Thompson, who was arrested at around 7pm local time on Tuesday, two hours after the attack. He has been booked under two counts of attempted murder and two counts of elder abuse.
Investigators say they are looking into the motivation behind the attack and have not ruled out the possibility of racial motivation.
Patricia Lee, who works at the flower stand near the bus plaform and was one of the witnesses of the attack told a local ABC TV station: “It was a pretty big knife, it had knuckles on the handle and the blade had holes in there like a military knife.
“He walked right next to me — I could have been the one who got stabbed.”
Over the last few months, attacks against Asian Americans have increased severely in the US.
On Sunday night, a 50-year-old man attacked two Asian American women with a cinder block in West Baltimore.
Another attack took place outside a grocery store in San Francisco this week when a man and his one-year-old child were attacked.
According to a research released by reporting forum Stop AAPI Hate Crime in March this year, nearly 3,800 incidents of hate crimes against Asian Americans were reported over the course of roughly a year during the pandemic.