The world number 19 led 6-3 5-7 6-2 4-6 5-4 against Carlos Berlocq, a stand-in for the absent Juan Martin del Potro, when he pulled his left hamstring after a four-hour marathon played in more than 35 degrees heat.
World number two Juan Monaco was looking to put Argentina 2-0 up on the first day at Parque Roca when he faced Florian Mayer in the second singles.
"I can't move my leg. I can't take a single step," Kohlschreiber told German reporters in the privacy of the locker room as he waited for a pair of crutches to be able to leave the claycourt stadium on the outskirts of Buenos Aires.
"It was a bitter thing for me and the whole team," added the 29-year-old. "It's hard to assess the gravity of the injury until further studies are conducted."
Argentina, normally favourites at home, had started the tie as underdogs given world number seven Del Potro's decision not to play the Davis Cup this year to concentrate on the tour and David Nalbandian's six-month injury layoff.
"I can't believe I'm experiencing this (win)," an elated Berlocq, ranked 70, said in a courtside interview.
"The whole (Argentine) team had drummed into me that I could win and at times I looked at the clock and thought 'I'm doing well because I'm tiring him and he has to play all three days'.
"Thank God, I got another chance after the defeat against (Tomas) Berdych," added Berlocq, who would not have played but for Del Potro's absence.
His loss to Berdych gave Czech Republic their semi-final victory at Parque Roca last September in the Argentine player's Davis Cup singles debut.