Trent Boult played a cameo of 38 as he helped New Zealand take 183-run first innings lead against India on Day three of the first Test.
Finn only made the current tour when he was added to the squad in place of the suspended Ben Stokes.
Moeen Ali scored 149 runs and took two wickets as England crushed Pakistan by 141 runs in the third Test at Edgbaston to take 2-1 lead in four-match series
Sohail Khan snared five wickets as England were all out for 297 on first day of the third Test against Pakistan at Edgbaston. Catch highlights of England vs Pakistan here
Fifties from both Kaushal Silva and Dimuth Karunaratne helped Sri Lanka end day two of the third Test against England on 162/1. Earlier, Jonny Bairstow's magnificent hundred guided England to 416 in their first innings
Steven Finn, who was ruled out of this year's World T20 in India due to an injury, will feature in England's playing XI for the first Test against Sri Lanka, starting Thursday.
Steven Finn, was ruled out of this year's World T20 in India due to injury, however, felt a decision on his fitness had been made prematurely
Steven Finn was ruled out with a strained left calf and his place in England's 15-man squad will now be taken by Yorkshire fast bowler Liam Plunkett.
England have brought in Liam Dawson as part of the squad for the 2016 ICC World Twenty20 while Steven Finn, who missed the limited-overs leg of the South African tour due to injury, has also been included in the squad.
Stuart Broad, who gained the number one spot in the world Test rankings, has not played international limited overs cricket since last year's World Cup.
Steven Finn, who suffered a side strain in the third Test, has been ruled out for the remainder of the South Africa series and will be replaced by Liam Plunkett.
South Africa slipped to 225 for seven before Chris Morris and Kagiso Rabada took them to the close with an unbeaten partnership of 42.
Hashim Amla, the South Africa captain, eased the pressure on himself and his top-ranked team with his 24th Test century, and first since December 2014.
Moeen Ali and Steven Finn helped England bundle the Proteas out for 174 as the hosts were thrashed by 241 runs. England are 1-0 up in the four-Test series and there are plenty of problems heading into the second Test.
Steven Finn picked up the crucial wickets of Dean Elgar, Hashim Amla and Faf du Plessis
Pacer Steven Finn and all-rounder Ben Stokes are returning from a foot injury and shoulder injury respectively. They have been named in England's 15-member squad for South Africa series, starting on February 3
Steven Finn was initially left out of the 16-member England squad for the South Africa series after developing a bone stress injury during the part of the Test series against Pakistan.
Steven Finn is yet to regain full fitness following a bone-stress problem while Mark Wood is nursing an ankle injury. Both players were not part of England's squad for Pakistan series