The store opened in the city of Ahmedabad in Gujarat 10 days ago.
Its owner says he did not know who Adolf Hitler was and the store is named after a business partner's grandfather who was called Hitler for being strict.
Mrs Sagiv said she would "raise the issue" with the state government next week during a pre-arranged visit to Gujarat.
"I don't think they have named the store out of malice, I think it's just ignorance and insensitivity on their part," she said.
The shop's owner Rajesh Shah, who sells men's clothing, said he was surprised he had upset people.
"I didn't know how much the name would disturb people," he told the AFP news agency.
"It was only when the store opened I learnt that Hitler had killed six million people."
Mr Shah said he would change the store's name if he was compensated for re-branding costs.
He said he had spent 150,000 rupees (about $2,700; £1,700) on the logo, hoarding and business cards.
The store has Hitler written in large letters over the front and a Nazi swastika symbol makes up the dot on the letter "i".
Correspondents say the German dictator who took the world to war in the middle of last century is admired by a small but growing number of Indians.
Books on his life and Nazi memorabilia have found a steady market in some sections of Indian society where Hitler is admired, mostly by young people.