As with most things like this, the answer is "yes, but...". BSD can do it, but it isn't the same as how Linux does it, so if you're world is Linux, BSD is a trip to a foriegn land. BSD makes it straightforward to build minimal, fixed-function systems (and has for a very long time). There isn't, however, a point-n-click or other easy interfaces to do it. It requires somewhat more intimacy with how BSD systems are put together at a macro level. I think the investment is worthwhile; BSD makes it easy to understand the dependencies required and what can be left out. But I'm obviously in the minority.
And if you think Docker is cool as a mechanism to deploy these minimalist environments, check out what Jails in FreeBSD brings to the table with (since 2000, btw).