The two sides are due to play at Middlesbrough on Saturday with the second leg at St Mary's on Tuesday.
"Southampton Football Club has today been charged with a breach of EFL Regulations, and the matter will be referred to an Independent Disciplinary Commission," the EFL said in a statement.
"This follows a request from the EFL for the club’s observations after a complaint from Middlesbrough relating to alleged unauthorised filming on private property ahead of the two clubs meeting (on Saturday)."
The EFL referred to regulations barring clubs from "observing, or attempting to observe, another club’s training session within 72 hours of a scheduled match between the two clubs."
The League said Southampton would normally have 14 days to respond but in this case it would ask the Independent Disciplinary Commission to list a hearing as soon as possible.
There was no immediate comment from either club.
Hull City and Millwall played the other semi-final first leg on Friday with the score ending goalless. They play the second leg in London on Monday.
Millwall finished the season third overall with Southampton fourth, Middlesbrough fifth and Hull sixth.
Champions Coventry City and runners-up Ipswich Town have secured automatic promotion to the Premier League.