It is not clear how long the defender will be out for, but it comes as another blow to Anfield boss Brendan Rodgers.
Liverpool injury nightmare
The Liverpool manager was upset during the previous international break when Daniel Sturridge returned from England duty with an injury. He has missed seven games with the thigh complaint.
England v San Marino preview
Other Liverpool players injured while on international duty include Wales midfielder Joe Allen and German under-21 international Emre Can.
So the news that Lovren has picked up a muscle tear with Croatia will not be welcomed at Melwood training ground.
A statement on the Croatian Football Association website reads: "During training on Wednesday Lovren felt pain in the abdominal wall.
"Igor Boric [a specialist] at St Catherine Hospital showed there was a tear and he will not be ready for performances in Sofia and Osijek."
Lovren will now leave the Croatian training camp and return to Liverpool for assessment and treatment, although it's not clear how many, if any, games he will miss.
Without the former-Southampton centre-back Rodgers will be forced to call upon his last two fit senior defenders, Martin Skrtel and Kolo Toure.
Croatia had been set to play Lovren against Bulgaria and Azerbaijan in their European Championship qualifiers. The talented defender was one of the breakout players in the Premier League last season, and formed a key part of Southampton's impressive rise to eighth in the table.
He asked for a move away from the south coast after a single season after he saw the likes of Adam Lallana and Luke Shaw depart for top five clubs, and Southampton received £20m from Liverpool for his services.
Southampton paid Lyon around £8m for him in the summer of 2013.
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