The chief of India's second largest IT services firm also discussed with Mr Modi ways in which the company can participate in the Prime Minister's vision of smart and digitally empowered India.
Infosys will develop software for managing the 'Kumbh Mela' scheduled in Ujjain (Madhya Pradesh) in 2016, he told PTI in an interview.
Mr Sikka, the first non-founder CEO of Infosys, said Mr Modi has agreed to dedicate the company's Mysore campus as the first model smart city in the country in April this year.
"Today, I had a meeting with the Prime Minister. We had a talk on smart cities, smart infrastructure, which is close to his heart."
"And the other big area is innovation. PM has a vision for innovation. As announced last week, we have a $500 million Innovation Fund. Of this, we have decided that half of this, which is a little over Rs 1,500 crore, will be dedicated to just innovation in India. We will call it Innovate in India," Mr Sikka said.
On smart cities, he said Infosys campuses are one of the most amazing places in the world. They are green and energy efficient and work as smart units, he added.
"Our Mysore campus is a small smart city. It has 30,000 people living and working there at any given day. We are going to make our Mysore campus the first model smart city and the PM has very graciously accepted our invitation to the Mysore campus and dedicate it to the nation in April," Mr Sikka said.
Spread over 350 acres, Infosys's Mysore campus, which also houses its university, has more than 200,000 trees and is energy-efficient.
"We want to make this a part of PM's vision for smart, digital and swacch India. Everything is digital, it is completely digital (referring to the campus, including toilets)," Mr Sikka further said.
Elaborating on the discussion around the Kumbh Mela, he said after the meeting, the teams have already started brainstorming on the solutions.
"Ujjain is very close to where I was born. I was born in Shajapur in Madhya Pradesh and we will be very happy to do that. We have been thinking about how we will do this, to make software for the kumbh mela, clean toilets. It was a very very productive meeting," he said.
The Infosys CEO added that the company will look at offering software for participants and organisers.
"Clean toilets is (also) one of them (initiatives) as lakhs of people will be using them, things like self-cleaning toilet, water free urinals, etc.," he said.
Former SAP board member Mr Sikka who spent his growing years in Gujarat, said he shared his nostalgia about 'Uttarayan' (Makar Sankranti in other parts of the country) with PM Modi.
On his Budget expectations, Mr Sikka said the government should make the environment business friendly.
There is an increasing role that the government can play in ensuring a smooth flow of ideas and skill. "Our expectations would be to make, tax, tariff structure and trade easier," he added.
Infosys later said in a statement that it will use the Innovation Fund to invest in India's young companies innovating in next-generation solutions and technologies like artificial intelligence, automation, pervasive connectedness as well as collaboration and design technologies.
It further said it will invest in great Indian start-ups, help amplify their engineering and operations, as well as help bring their innovations to market at scale.
The Bangalore-based firm also said it will provide its expertise in the areas of smart infrastructure planning and sustainable building technology to the Ministry of Urban Development.
The concept of a smart and sustainable city is based on leveraging the power of data and the latest technologies in building and use of IT to minimise energy and resource consumption, increase the use of renewable energy, and reduce and manage waste effectively.
Shares in Infosys, on Wednesday, ended almost 2 per cent up at Rs 2,128.80 apiece on the BSE.