After we clean the baby bottles, which have had baby formula (milki), we put them inside a container with 200ml of water and heat it in the microwave for 3 minutes. We use this microwave for meat products.
Is there a problem of sterilizing the baby bottles inside a close container in a meat microwave?
If I understand your question correctly, you are placing the clean milky bottles inside a container, closing the container and putting it into a meaty microwave.
It is permitted to do, but be careful that the cover is closed well. The reason for this is that using a microwave for milk and meat separately is controversial, and not recommended. In your case the bottles do not have any milk in them, and the milk that was absorbed inside them should only be kli sheini. Therefore we are not going to worry that the minute amount of absorbed taste is going to mix with the steam of the meaty microwave, since the container is closed. See sources
Regarding sing a microwave for milk and meat separately, there are two issues. The first is that the container may open and the hot steam will mix with the meaty residue on the walls of the microwave. The second issue is that l’chatchila we don’t want a milky vessel to touch a meaty one, even if there is no liquid in between them. Therefore there are different opinions if we may cook something milky in a closed container in a meaty microwave. Some poskim permit it, if the container is closed well, and the dish under the switched for a milky one. Others say not to do it at all because of the risks involved. See Shvus Yitzchok 6- pg. 51, in the name of R’ Eilyashiv and R’ S. Z. Auerbach zt”l not to use a microwave for milk and meat even if both are used when covered. So is theopinion of R’ Vosner zt”l (M’bais Halevi 3 pg. 22), Zera Shemuel Basar Bechlav ftnt. 242 in the name of R’ Y. Berkowitz shlit”a that it isn’t l’chatchila to do. On the other hand see Pischei Halacha pg 233, R’ B. Forst shlit”a that if both the meaty and milky are covered then it is permitted. Also see Yivakesh Torah, siman 11-39, and Kovetz Ohr Yisroel 5-13(8) that if it is covered and it has a different plate underneath it then it is permitted.