Lt. Gov. Dan Patrick, a top social conservative voice in the state, unveiled the proposed law Thursday at a news conference.
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Patrick says the "Privacy Protection Act" is a top priority for the GOP-controlled Legislature, which convenes next week.
Lawmakers likely will support it, even though Texas' largest business lobbying group says it and other anti-gay rights proposals could cost the state up to $8.5 billion and 100,000-plus jobs.
North Carolina faced boycotts, and potentially billions of dollars in lost state revenue, after passing its own version last year.
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A Virginia lawmaker introduced similar legislation this week.