What are the qualifications typically found in textbook authors? Is a Ph.D. in the field a "must," or do some people write textbooks who hold Masters degrees (yet not a Ph.D.)?
There are no rules for this in terms of minimal qualification. Why would there be? Readers want good books. Publishers want to sell books. Who cares if the author has a PhD or not?
In fact, trying to get deeper, it's often difficult to define precisely even what is meant by a "textbook" in the intuitive sense you probably mean.
For example, would books in the O'Reilly Media series be considered textbooks? Would instructional e-books? Etc.
As such the answer depends widely on the publisher or the book series (if any) you wish to contribute to.
For book series, there is typically an editor in charge who will make a judgement call on whether or not you are qualified and whether or not you can contribute something good to the series.
If dealing directly with a traditional academic publisher (I'm thinking of the likes of Springer), you (and your book proposal) will again be evaluated by their editorial staff before they agree to a contract. Likewise, they will only publish the book pending review by a number of experts that you propose.
But again, it varies widely.
In summary: I think if you have enough genuine material for a textbook -- material that people want to read -- you could find a reasonable publisher even without a Masters/PhD.