The two forwards were forced off during a frantic first half in Amsterdam, with Havertz replaced after 30 minutes and Brobbey departing shortly afterwards.
Havertz appeared to suffer the problem after being caught on the knee by a high boot from Netherlands midfielder Quinten Timber. The Arsenal forward received treatment before being replaced by Younes Ebnoutalib, who was making his Germany debut.
Brobbey's injury appeared to be muscular. The Sunderland striker pulled up while attempting to press for the ball and subsequently indicated a problem at the back of his thigh. Further tests are expected to determine the extent of the injury.
The timing was particularly unfortunate for Brobbey after he had scored a hat-trick in Sunderland's remarkable 5-3 defeat against Manchester City at the weekend.
Germany took the lead through Felix Nmecha after the Netherlands had been angered by the decision to allow play to continue while Brobbey remained on the ground.
Cody Gakpo eventually rescued the hosts, volleying home in stoppage time from Ruben van Bommel's cross to deny Klopp victory in his first match in charge.
Klopp was encouraged by aspects of Germany's performance despite the result.
“We have to accept the result. Even though I badly wanted to win I take the draw.”
“I was very, very, very pleased with a lot of the individual performances. Overall, I was very happy with the passion we showed. We can play better and play more football, that's for sure.”
The match also marked Xavi's first game as Netherlands manager after his appointment to replace Ronald Koeman.
Van Bommel, who supplied the equaliser, became the third generation of his family to represent the Netherlands after his father Mark van Bommel and grandfather Bert van Marwijk.
For Klopp and Xavi, the result provided an intriguing opening to their international careers, but the fitness of Havertz and Brobbey will now be a bigger concern for their clubs and national teams.
The extent of both injuries remains unclear, with further medical assessments required before either player's availability for the remainder of the international window can be established.