The 27-year-old played the full 90 minutes of his country's resounding 3-0 Nations League win over Germany on Saturday, opening the scoring with a 30th-minute header before Memphis Depay and Georginio Wijnaldum added in the second half.
He will hope to recover in time for Liverpool's Premier League visit to Huddersfield Town on Saturday, having been passed fit to play in the last game against Manchester City despite carrying the knock.
The news comes as a blow for Netherlands after the defender's role in a result against Germany that he admitted afterwards he could not have imagined.
"Germany are not just a team. They are top quality players who play at top clubs," he told NOS on Saturday night.
"You don't expect a result like that in advance. If you had said before that we would beat Germany 3-0, nobody would have believed you.
"It feels very good, we worked hard, won 3-0, kept the clean sheet, that is very nice. The 2-0 goal [from Depay] was important, then I thought it was game over."
Van Dijk has been an ever-present at the back for Liverpool so far this season, starting all eight of their Premier League matches, and will hope to shake off the injury in time to face Huddersfield on Saturday.
Indeed, speaking to reporters after the match he insisted that Jurgen Klopp would be pleased that he didn't get injured during the win over Germany.
Mohamed Salah, meanwhile, has also returned to Merseyside after suffering an injury while playing for Egypt against Swaziland but the problem is not thought to be serious and he too will hope to recover for the weekend.
Jurgen Klopp's Reds are currently third in the Premier League table after eight matches and are level on points with both Manchester City and Chelsea.