Solar Impulse 2 took off in the early hours of March 19 from Varanasi, India on route for Mandalay.
The flight piloted by Mr Bertrand Piccard is expected to take 16 hours before it lands in Myanmar, according to the team.
The aircraft landed in the Hindu holy city of Varanasi on March 18 for an overnight stopover after its pilot launched an angry attack on Indian bureaucracy following a lengthy hold-up in Prime Minister Narendra Modi's home state.
Mr Piccard, one of the two Swiss pilots of the solar-powered plane, said he and his team had been frustrated by delays over paperwork in Ahmedabad city in the western state of Gujarat.
The plane landed in Ahmedabad last week from the Omani capital Muscat after completing an initial sea crossing in its epic bid to become the first plane to fly around the world solely powered by the sun.
The single-seater had been due to leave on March 15 for a short flight to the Hindu holy city of Varanasi before heading onto neighbouring Myanmar on March 19.
But the plane, flown by co-pilot Mr Andre Borschberg, could only leave on Wednesday morning after delays blamed on bad weather, while Piccard's support team remained stuck at Ahmedabad airport hours after takeoff.
"The delay is (because) of administration, papers, stamps," Mr Piccard told reporters at Ahmedabad airport.
"I'm not here to accuse anybody. I just say that since the last five days we are trying to get all the stamps and every day (they) say tomorrow," said Mr Piccard.
"Since five days we are desperate to get all the stamps and we still have stamps missing."
Solar Impulse 2 later arrived in Varanasi, touching down shortly after 8:30 pm local time (1500 GMT) after over 14 hours of flying, according to its official Twitter handle.
Mr Piccard's team needed to arrive in Varanasi ahead of Solar Impulse 2 to coordinate its landing.
The team had posted pictures on Twitter of themselves at Ahmedabad airport looking anxious and miserable, before finally getting the go-ahead to leave hours later.
Another picture shows a smiling Piccard holding up his passport with stamps in it.
Mr Piccard's comments risk embarrassing Mr Modi, who has vowed to cut bureaucratic red tape in promised reforms to revive India's economy after storming to power at general elections last May.
Additional reporting from AFP