Does soy milk contain estrogen?

Not per se. Soy contains plant phytoestrogens which are weak (very weak) activators of the estrogen receptor. The word "estrogen" commonly refers to 17-beta-estradiol, the most potent of the estrogen receptor stimulators found in the natural human circulation.
No. Soy milk does not contain human estrogen, but it does contain plant estrogens.

Related Questions

Does soy milk help in alleviating hot flashes of premenopause? Any risks or side effects since it has plant estrogen in it? Weight gain?

Soy. Ingesting soy milk is probably fine. Soy is a weak phytoestrogen when ingested as a food product, though some drug companies use soy as a base for their estrogen product. Do some label reading though as some soy milks have additives that increase the calories. Adding soy beans to salads or eating tofu is also a good source of soy. Read more...