The presenter, 47, started the show as usual alongside co-host Charlie Stayt on Friday morning (18 November).
But some viewers noticed that she sounded as if she may have a sore throat, with one suggesting somebody could give her a Strepsil.
She then disappeared from the set and Stayt announced that she had "stepped away".
Sitting on the sofa alone, he said: "You may have noticed this morning that Naga has just stepped away from the sofa for a minute for a slight struggle with her voice.
"So we'll see how that works out."
Viewers had noticed that Munchetty didn't seem herself and had been posting messages about it on Twitter.
"What is Naga Munchetty doing in the studio today, she is clearly not well," one tweeted.
"Get well soon Naga," another said.
One remarked: "Bless Naga. I wasn't looking at TV, didn't realise it was our lovely Naga. I thought that @BBCBreakfast presenter sounds like Gonzo! She needs bed rest and some honey & lemon."
"Hope Naga is OK," said another fan.
Somebody else said they thought Munchetty was "certainly looking uncomfortable earlier and not up to reading as many headlines".
"Naga has lost her voice," said one fan.
However, once Munchetty had left the programme some viewers were confused about her absence.
"What's happened to Naga she was on the soda at 6am and now she has gone?" asked one baffled viewer, who clearly missed Stayt's explanation.
Yahoo has contacted the BBC for comment.
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