Etymology of the phrase "Dependency injection" in computer science
It was almost certainly Martin Fowler who coined the term, and other responders have pointed to its first use in publication.
The reason for the choice of term appears to be that the concept of 'injection' was relatively new at the time. Other ways of getting a dependency in a class, such as inline instantiation, are essentially 'creation within', rather than 'insertion from the outside', which is what was new about this concept in the history of best practices for the writing of maintainable code - hence Fowler's 'injection'.
EDIT
This article, written in 2004, is the earliest known usage of the phrase: http://www.martinfowler.com/articles/injection.html#FormsOfDependencyInjection
The concept itself, previously known as the 'Dependency Inversion Principle', was first created by Robert C. Martin, in the mid-90's: http://www.objectmentor.com/resources/articles/dip.pdf