"I do really just hope for Daniil," triple champion Hamilton told reporters at a Spanish Grand Prix news conference that also featured Kvyat and his Dutch replacement Max Verstappen.
"We’ve got two fantastic drivers here," added the Mercedes driver.
"I just hope that in this manoeuvre it doesn’t hinder either of their careers because they’ve got bright futures ahead of them and too much pressure, too much stress, too much expectation too early on can lead the wrong way."
Red Bull announced last week that Kvyat, 22, was being sent back to feeder team Toro Rosso in a swap with the 18-year-old Verstappen.
The Russian had moved up to Red Bull after one season with Toro Rosso in 2014.
Hamilton, who made his debut with McLaren in 2007 and won his first title with them in 2008, said it worked well for him to go straight into a big team but some drivers took longer than others to adjust.
"I think ultimately it's a good opportunity for one and for the other very unfortunate," he said of the Red Bull swap.
"Red Bull has done well in bringing young talent forwards but I think they need to be aware that young drivers need time to progress. Mistakes do happen, there's so much pressure on drivers, particularly at a young age."
Kvyat's demotion came after he collided twice with Ferrari's Sebastian Vettel, a four-times champion with Red Bull, at his home Russian Grand Prix. The Russian had been on the podium in the previous race in China.
Spain's double champion Alonso, who started out with now defunct tail-enders Minardi before a move to Renault, also hoped Kvyat and Verstappen could have a long future in the sport.
"They have the potential talent to be Formula One world champions one day and I really hope the best for them," said the McLaren driver.
(Editing by Clare Fallon)
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