Doctors found the tumours are "quite big" and advised her biopsy to check on possible malignancy.
The biopsy report is expected to come on Monday, bdnews24.com reported.
51-year-old Taslima's mother had died of cancer and her brother is also undergoing cancer treatment in New York.
She arrived in New York a week ago to give a lecture on "women in secularism".
But, when she was diagnosed with breast tumours, Taslima expressed her worries on Twitter:
After 8 hours,at 9 am I'll get my breast tumour biopsy reports. I have no idea what is awaiting me. I should try to sleep now. Love you all.
After 8 hours,at 9 am I'll get my breast tumour biopsy reports. I have no idea what is awaiting me. I should try to sleep now. Love you all.— taslima nasreen (@taslimanasreen) May 12, 2014
Besides an acclaimed author, Taslima is also a doctor and accompalished her MBBS from Mymensingh Medical College in 1986.
After her novel 'Lajja' (Shame) hit the stands, she incurred the ire of the fundamentalists and had to leave Bangladesh in 1998. [Read More]