In an interview on Monday, Mr Trump had said Mrs Merkel had made an "utterly catastrophic mistake by letting all these illegals into the country".
But Anthony Scaramucci said the incoming president had an "enormous amount of respect for her".
Mr Scaramucci also told the BBC the US would win a trade war with China.
Speaking at the World Economic Forum in Davos, Mr Scaramucci said that Mr Trump had been "trying to be complimentary" about Mrs Merkel.
Davos coverage in full
Mr Scaramucci, who will enter the White House on Friday as a senior adviser to the president, acknowledged that Mr Trump's comments had been received by many as an attack on the European community, but dismissed reports of a feud between the US and German administrations.
"You shouldn't be worried," he told the BBC.
"We have a very longstanding, very close cohesive relationship with western Europe and that will remain in place during the Trump administration."
In the controversial interview with The Times and Germany's Bild, Mr Trump also appeared to put Russia's Vladimir Putin and Chancellor Merkel on an equal footing, saying he would "start off trusting both".
But Mr Scaramucci denied that the president-elect was being disparaging of Mrs Merkel.
"He was basically saying that he holds her in a tremendous amount of respect, but she may have made some mistake as it related to the influx of immigration, which from what I have read from the German press, she has admitted to. So I don't understand why this is such an international outcry."
Mr Scaramucci, who is the only member of the Trump administration to attend this year's World Economic Forum, also predicted that European leaders would warm to the incoming president.
"Over the next two to three yearsâ€¦ I think Chancellor Merkel will respect the strength of President Trump. I think she will have a great relationship with him."
One of Donald Trump's closest advisers has told the BBC the US president-elect's criticism of German Chancellor Angela Merkel has been misinterpreted.