The duo will lead a delegation of policymakers and businesses including fintech firm TransferWise in Delhi and Mumbai.
Baroness Neville-Rolfe, the commercial secretary, and Mark Garnier, international trade minister, will also join Hammond and Carney on the trade mission.
Hammond said: "I'm delighted to be leading such a heavyweight delegation to India to bang the drum for British business.
"I am determined to create a truly global Britain, reaching out and promoting the best of what we have to offer.
"As we leave the EU and embark on an exciting new phase of our economic history, looking to boost our trade and investment beyond the borders of Europe and strengthening our relationships with the world's most vibrant economies is more important than ever."
Hammond added that the UK is "perfectly placed to be India's financial partner of choice".
"Our innovative markets have helped support the development of whole new product classes such as masala bonds that will support India's transformation."