"email warning" is correct and usable in written English.
You may use it when referring to a warning that is sent via email. Example: I received an email warning that I had exceeded the data allowance on my phone plan.
"Our actions will speak for themselves," said the email warning.
I have just been sent an email warning me my PayPal account has been limited.
He recently received an anonymous email warning him that rumours were being circulated in legal circles that he was a drug addict.
Sixsmith denied that he rang journalists to tell them that special adviser Jo Moore was attempting to "bury" bad news about rail performance on the day of Princess Margaret's funeral, but admitted sending Moore an email warning her.
A few days before Christmas last year I checked my inbox and found a mysterious email warning me not to write the book with Yeon-mi and help "spread her lies".
Ticket-holders for this month's event got an email warning them not to bring alcohol in a "wheeled device".
Phillips is concerned about his family, concerned about his kid not doing too well in school, concerned about borderline-lax conditions aboard ship and concerned about emails warning of pirate attacks from Somalia.
Yet she still finds time to write a blog responding to queries from Google's loyal users, one of whom regularly sends emails warning that the number of words on the famously sparse homepage is creeping too far beyond 50.
People using Twitter to name the "celebrity threesome" couple have had emails warning them of legal complaints, just hours after the supreme court upheld a privacy injunction against the UK press on Thursday.
They're nervous about Barack Obama being a closet Muslim - they've heard it on right-wing radio, they've received emails warning them of this - and, since religion is so central to their lives, they're reluctant to vote for someone who doesn't share their beliefs.
General Petraeus was forced to resign as director of the CIA after his affair with Paula Broadwell, his biographer, was discovered by FBI agents when they identified her as the source of anonymous emails warning a glamorous military liaison officer, Jill Kelley, to keep her hands off Petraeus.
