The injury means Kashyap will not be able to participate in the three events in the country, starting with the India Open Super 500.
Lakshya Sen fought hard before going down to top seed Kento Momota of Japan.
Kashyap and Srikanth went down fighting in the opening round.
The Indian women's duo of Ashwini Ponnappa and N Sikki Reddy and men's doubles pair of Satwiksairaj Rankireddy and Chirag Shetty progressed to the second round with straight game wins.
Parupalli Kashyap exited from the tournament after he retired in the third game of his first-round clash against Canada's Jason Anthony Ho-Shue owing to a calf injury.
It was a chaotic day and the entire procedure put us under severe mental stress, the duo told Malayala Manorama.
They will compete in back-to-back BWF World Tour Super 1000 events in Thailand.
The withdrawal of former world No.1 Saina means there will be no Indian participation in the women's singles event at Odense as world champion P V Sindhu has already opted out.
On Tuesday, the BAI recommend doubles pair of Satwiksairaj Rankireddy and Chirag Shetty and men's singles player Sameer Verma for the Arjuna Award.
Kashyap pointed out that there is still no scope for practice amid the coronavirus pandemic and the BWF has drawn out a calendar made of 22 tournaments across the world in five months.