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This is a weird claim. Al-Khazraji, in his book نفس الصباح في غريب القرآن وناسخه ومنسوخه, volume 1, pages 250-251, says that some people have said

was abrogated by a Hadeeth reported by Abu-Daawood which prohibits being silent an entire day. He says that An-Nahhaas argued that if we accept that the laws of prior nations apply to us too, then 3:41 was abrogated. He says that not mentioning God an entire day is prohibited. Makki agrees that an abrogation claim may be made here.

Setting aside the authenticity of the hadeeth, and the established consensus that the hadeeth cannot abrogate the Quran, verse 3:41 does not prohibit Zachariah, peace be upon him, from mentioning God three nights; it simply tells him that for three nights, he will not be able to speak even though he won't be sick. God did not order Zachariah to be silent, He told him that his sign is that he will be silent. Therefore, there is no ruling here that we have to follow; it's a special situation that applied to Zachariah only and for that event only.

Furthermore, mentioning God does not have to be made by the tongue, per

If that weren't so, the dumb would have been deprived from mentioning God and the reward that accompanies it.

Lastly, the hadeeth was rated authentic by Al-Albaani only. Of the top six most regarded Hadeeth compilation books, none other than Abu-Dawwodd reported it.

For:
An-Nahhaas,
Makki (implied),
Al-Khazraji.

Against:
The majority, according to Makki,
Al-Qurtubi (implied as he said that 3:102 was the only abrogated verse in Chapter 3),
Dr. Mustafa Zayd.

This is a tough one to discuss without losing one's cool. 3:41 is the ultimate statement of fact: It is an account of something that has already happened. If it's abrogated, what does that mean? God didn't say that to Zakharia? This was allowed from the time of Zakharia until the referred-to hadeeth? What?