Praise be to Allah.

There is nothing wrong with calling the Quran holy (muqaddas), because what is meant by (the Arabic word translated here as holy) is pure.

Al-Azhari (may Allah have mercy on him) said: al-Quddoos (the Holy) – which is one of the names of Allah – means the Pure, the One Who is above all faults and shortcomings.

See: Lisaan al-‘Arab,

Ibn Jareer (may Allah have mercy on him) said:

The Arabic word taqdees, which means sanctifying (making holy), refers to purification and veneration. Hence the phrase “subbooh qudoos (glorified, holy).” What is meant by subbooh is declaring Allah to be above all faults. What is meant by quddoos is declaring His purity and venerating Him. Hence the land is called ard muqaddasah (holy land), i.e., it is pure. What is meant by the angels saying Nahnu nusabbihu bi hamdika (We glorify and praise You) is: We declare you to be above anything that the polytheists attribute to You, and we pray to You. Nuqaddisu laka (We proclaim Your holiness) means we affirm all Your attributes, and We affirm that You are pure and free of all impurities and all that the disbelievers ascribe to You. End quote.

Tafseer at-Tabari.

But it is more appropriate to describe the Quran as Allah, may He be exalted, has described it, as He says (interpretation of the meaning):

“These are the Verses of the Book, and a clear Quran”

[al-Hijr 15:1]

“And indeed, We have bestowed upon you seven of Al-Mathani (the seven repeatedly recited Verses), (i.e. Soorat Al-Fatiha) and the Grand Quran”

[al-Hijr 15:87]

“(This is) a Book (the Quran) which We have sent down to you, full of blessings”

[Saad 38:29]

“Ya-Seen. By the Quran, full of wisdom (i.e. full of laws, evidences, and proofs)”

[Yaa-Seen 36:1-2]

“That (this) is indeed an honorable recital (the Noble Quran)”

[al-Waaqi ‘ah 56:77]

“Nay! This is a Glorious Quran,”

[al-Burooj 85:21].

We should not give the Quran the title of “the Holy Quran” lest we be like the Christians who call their distorted and altered book “the Holy Bible”.

But if it is asked, is the Quran a holy book? We say: Yes, and it is the most deserving of being called holy and pure, and being described as superior to all other books. But we do not call it the Holy Book or the Holy Quran, so as not to resemble the Christians in that regard. Even though it may be described as being holy or pure, it should be given the names that Allah gave to it and with which He described it, so we should say the clear Quran (Quran mubeen), the Quran filled with wisdom (Quran hakeem), Noble Quran (Quran kareem), Glorious Quran (Quran majeed).

And Allah knows best.

(Source - Islam Q&A)