Banerjee, who arrived in Bhubaneswar on Tuesday evening on a three-day tour to the state, went straight from Biju Patnaik International Airport to Apollo Hospital here to meet Bandyopadhyay.
"Our MP Sudip Bandyopadhyay is unwell.
I have come to see him," the West Bengal Chief Minister told reporters here.
TMC Parliamentarian Sudip Bandyopadhyay has been arrested by the Central Bureau of Investigation (CBI) for his alleged links with the Rose Valley chit fund scam. Another TMC MP Tapas Pal was also arrested by the CBI in the chit fund scam.
Banerjee also said that she would meet Odisha Chief Minister Naveen Patnaik if time permits.
"I also wish to visit Puri to pay obeisance to Lord Jagannath," she added.
The West Bengal Chief Minister will visit Srimandir on Wednesday morning.