It is essential to differentiate between the two kinds of beer:
The first is the intoxicating beer that is sold in some countries. This beer is khamr (an intoxicant) and it is haraam to sell it, buy it and drink it. The Prophet (peace and blessings of Allaah be upon him) said: “Every intoxicant is khamr and every intoxicant is haraam.” Narrated by Muslim, 2003.
It is haraam to drink a lot or a little of it, even a single drop, because the Prophet (peace and blessings of Allaah be upon him) said: “Whatever intoxicates in large quantities, a little of it is haraam.” Narrated by al-Tirmidhi, 1865; classed as saheeh by al-Albaani in Saheeh al-Tirmidhi.
The second type is beer that is not intoxicating, either because it is completely free of alcohol, or because it contains a minuscule amount of alcohol that does not reach the level of causing intoxication no matter how much a person drinks of it. The scholars have ruled that this is permissible.
Shaykh Ibn ‘Uthaymeen said:
The beer that is on sale in our marketplaces [in Saudi Arabia] is all halaal, because it has been inspected by the officials and is completely free of alcohol. The basic principle concerning all kinds of food, drink and clothing is that they are permissible until and unless proof is established that they are haraam. Allaah says (interpretation of the meaning):
So if anyone says, this drink is haraam, or this food is haraam, or this garment is haraam, say to him, Bring your proof. If he brings proof then we should do whatever is indicated by the proof. If he does not bring proof, then his words are to be rejected, because Allaah says (interpretation of the meaning):
Everything in this world Allaah has created for us. This general meaning is confirmed by the word jamee’an (translated here as “all”). And Allaah says (interpretation of the meaning):
So if something is haraam, there should be a clear and detailed indication that it is haraam. If there is no such proof then it is not haraam. The beer that is to be found in our markets here in the Land of the Two Holy Sanctuaries (Saudi Arabia) is all halaal and there is no doubt concerning that in sha Allaah.
We do not think that any alcoholic content in a thing makes it haraam, rather if something contains a percentage of alcohol which will make a person intoxicated if he drinks it, then it is haraam. But if the amount is miniscule and does not have any effect, then it is halaal.
Some people think that the words of the Prophet (peace and blessings of Allaah be upon him), “Whatever intoxicates in large quantities, a little of it is haraam”, mean that if a small percentage of an intoxicant is mixed with a large amount of a substance that is not intoxicating, then it is haraam. This is a misunderstanding of the hadeeth. “Whatever intoxicates in large quantities, a little of it is haraam” means that if a lot of something will cause intoxication, and a little of it will not cause intoxication, then a lot or a little are both haraam, because you may drink a little that does not cause intoxication, then you may be tempted to drink more and become intoxicated. But if something is mixed with alcohol but the alcohol is a small amount and does not have any effect, then it is halaal and does not come under the ruling of this hadeeth.
Al-Baab al-Maftooh, 3/381-382.