Troughton, who plays Edmund opposite Simon Russell Beale's Lear in Sam Mendes' production, was reportedly "struck dumb mid-sentence" shortly before the interval during Tuesday's performance.
Russell Beale told the BBC: ""It must have been terrifying. Apparently his voice just completely gave out."
As a result of the incident, the actors had to "nip and tuck" some of the remaining scenes in the first half to omit Edmund's lines.
"Various actors had to do monologues - so it was rather skilful," added Russell Beale.
Mendes took to the stage at the interval to explain that the understudy Paapa Essiedu would take over the role for the second half.
He reportedly told the audience: "you are in the privileged position of seeing not one but two actors nightmares," referring to both Troughton and Essiedu.
The cast also features Kate Fleetwood, Anna Maxwell Martin and Olivia Vinall as Lear's three daughters Goneril, Regan and Cordelia, alongside Adrian Scarborough as The Fool and Stanley Townsend as Kent.
The production marks former Donmar Warehouse artistic director Mendes' first return to the National Theatre since 1998.
This article has been updated after the National contacted WhatsOnStage to confirm that Sam Troughton will return for tonight's press performance