The European group, which directly employs nearly 15,000 people, warned that crashing out of the bloc would be "catastrophic" and force it to consider its investments.
"Put simply, a 'no deal' scenario directly threatens Airbus' future in the UK," said chief operating officer Tom Williams.
May's government holds out the possibility of walking away as a negotiating tactic, but says she expects to get a deal before it exits the bloc on March 29 next year.
"We have made significant progress towards agreeing a deep and special partnership with the EU to ensure trade remains as free and frictionless as possible, including in the aerospace sector," a spokeswoman said.
However, talks are stalled on the issue of the Irish border and Britain's indecision over what it wants.
EU leaders, who will meet May at a summit next week, have warned that time is running out, while Brussels has urged them to step up preparations for no deal.