Yorkshire's Plunkett is struggling with discomfort in his left ankle which he first felt at the end of the second Test at Lord's, which India won by 95 runs despite the former Durham man taking four wickets in the game.
He did not play in the third Test at The Ageas Bowl, where England won by 266 runs to level the five-match series at 1-1.
While England already have James Anderson, Stuart Broad, Chris Jordan and Chris Woakes in the squad as specialist pace bowlers as well as all-rounder Ben Stokes, Finn has been handed a recall to add further cover.
Finn has played 23 Tests for England, the last of which came against Australia in July 2013. He was dropped after the first Test although he travelled to Australia for the following Ashes series in the winter just gone.
However, following a difficult time on the fringes of the team he returned home in January and has benefited from playing a full part in Middlesex's season to force his way back into contention.
This season, he has taken 44 wickets in the LV= County Championship, helping Middlesex set the early pace, as well as four wickets apiece in Twenty20 and one-day competitions, the former of which saw him make just four appearances, and the latter of which has only just got underway.
The third Test begins on Thursday (7th August).
England Test squad: Alastair Cook (captain), Moeen Ali, James Anderson, Gary Ballance, Ian Bell, Stuart Broad, Jos Buttler, Steven Finn, Chris Jordan, Sam Robson, Joe Root, Ben Stokes, Chris Woakes
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