Udana endured the injury blow in the fourth over of the India innings while fielding at short third man.
He immediately withdrew from the field and did not take part in the remainder of the T20 clash.
His services were dearly missed as Sri Lanka struggled to contain India's belligerent batting charge with the hosts eventually completing a comprehensive seven-wicket win.
Udana's absence depletes Sri Lanka's fast bowling stocks, causing the team management to ponder over either drafting in right-arm paceman Kasun Rajitha or an additional spinner in the side.
The 31-year-old, who was part of Paarl Rocks in their victorious Mzansi Super League campaign, is considered a vital cog in Sri Lanka's white-ball set-up.
Skipper Lasith Malinga had expressed disappointment on the untimely injury setback in the aftermath of his team's defeat.
Sri Lanka coach Mickey Arthur also confirmed the severity of Udana's back strain in the post-match press conference and cautioned against risking the left-arm seamer in fear of being rendered unavailable for future assignments.
India currently boast an unassailable 1-0 lead in the series following the washout in Guwahati.
They are firmly placed as favourites to win the third encounter scheduled to take place in Pune on Friday.