A BBC spokeswoman confirmed that 30 complaints had been made relating to the show, which Evans took over from veteran broadcaster Johnnie Walker this week.
She said: "We want to stress this is a tiny amount [of complaints] when you take into account that Radio 2 has an audience of more than 13m."
She also conceded that there had been criticism on the station's own message board, but added: "We would not encourage people to complain that way."
Even though Evans had been experiencing a revival in popularity over the last two years, including hosting The Brits and presenting his Saturday afternoon show on Radio 2, his appointment to the drivetime slot raised eyebrows among Walker's loyal fans.
Prior to his appointment, which reportedly nets Evans £540,000 a year, some fans were calling for Stuart Maconie to replace Walker, who has since moved to a Sunday slot on Radio 2.
Maconie, who has taken over Evans' vacant Saturday afternoon slot, frequently deputised for Walker and was considered more akin to his laid-back style and emphasis on music, rather than chat.
Among criticism from listeners on Radio 2's online message board is that Evans appears not to be as interested in music and more concerned with talking about himself.
One listener said: "Certainly a bad day for Radio 2 listeners who have this dire rubbish inflicted on them by a presenter whose ego is out of control, has no interest in music whatsoever, is unfunny and stumbles over long words. Music is now officially irrelevant on this travesty of a radio service."
Another added: "If Evans is the future of Radio 2 then Radio 2 hasn't got a future."
But not all listeners were critical and some messages do indicate that the future could be brighter.
"Chris is in excellent, confident free-flowing form. Such a refreshing change from the dreary old cheesy dribblers who've presented drivetime in the past," another listener wrote.
Evans has been shortlisted for two Sony radio industry awards this year, in the personality of the year and entertainment categories.
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