The two lone victims, aged in their 50s and 60s, were stabbed two days apart in streets a short distance from each other.
Scotland Yard believes the attacks could be linked, and have urged women in the area to remain vigilant.
On Sunday, a 57-year-old woman suffered “a number of stab wounds” in an attack in Parnell Road in Bow.
Officers were called to the scene just before 8.30pm and the woman was taken to hospital by paramedics. Her condition has not been disclosed.
It came after a woman in her 60s was attacked in nearby Chariot Close on Friday.
She required hospital treatment for her stabbing injuries, although they were not life threatening.
On Sunday, a 51-year-old man was arrested on suspicion of grievous bodily harm, although was later released under investigation pending further inquiries.
Detectives have appealed for the public’s help to identify the suspected knifeman.
Scotland Yard said: “In both cases the suspect is described as a black male, aged around 40s, of large build with big hair who flees the scene of the attack on foot.
“Police in Tower Hamlets are appealing for help from local communities to identify the suspect and urge the public, particularly women, to be vigilant.”
:: Anyone with information should call 101 quoting CAD 6062/26AUG18 or tweet information to @MetCC. They can also contact Crimestoppers anonymously on 0800 555 111.