The quote you are asking about is most commonly phrased as:

“Injustice anywhere is a threat to justice everywhere.”

It was said and written by Martin Luther King Jr., in his 1963 Letter from Birmingham Jail.

Your version (“injustice anywhere is injustice everywhere”) is a shortened or slightly misquoted form, but people using it today are almost always referring back to Martin Luther King Jr.’s original sentence and idea.

King’s point was that communities are deeply interconnected, so tolerating injustice in one place endangers justice in every other place as well.