Gareth Bale's opener was cancelled out by David Lopes before Van der Vaart was forced off towards the end of the first period at the Home Depot Center with what looked like a groin problem.
Walker followed the Dutchman down the tunnel in the second half, the England international having only just returned to action after recovering from a toe injury which ruled him out of Euro 2012.
It capped a far from ideal night for new Spurs boss Andre Villas-Boas, who watched as his defence was regularly prised apart at one end by a side missing David Beckham and Landon Donovan, while a glut of chances were missed at the other.
Given this was just Spurs' second pre-season outing - and that the Galaxy are in the middle of their MLS season - the significance of the result should not be overstated, but nevertheless the double injury scare has cast a shadow over their pre-season preparations.
Villas-Boas did, however, get the opportunity to take another look at Gylfi Sigurdsson following the Icelandic international's goalscoring debut in the 2-0 win over Stevenage last week.
The former Swansea midfielder, Villas-Boas's first signing as Spurs manager, played in an advanced trident alongside Van der Vaart and Bale and it was his expert delivery that set up the opening goal on 17 minutes.
Sigurdsson's pinpoint pass from the left found Bale's head, although the Welshman - whose participation may well have raised eyebrows back in London, given that he pulled out of the British Olympic team with a back injury - still had plenty to do.
Otherwise, Sigurdsson flitted in and out of the action until his departure in the second half as another summer signing, Jan Vertonghen, struggled alongside Younes Kaboul in the heart of Spurs' defence.
Time and again the pair were beaten by long balls and only some profligate finishing from former Spurs striker Robbie Keane prevented the visitors from shipping more than one goal during the first half.
It came as no surprise when the equaliser arrived on 28 minutes, Lopes looking more like a striker than the central defender he is with a storming finish after Spurs were opened up by Marcelo Sarvas and Hector Jiminez. Brazilian Lopes met the latter's first-time cross from the right to crash the ball into the back of the net.
Keane then gave a reminder of why his Premier League career is unlikely to be rekindled with first some dithering play and then an unconvincing finish when twice played through on goal.
Jermain Defoe too had chances to give Spurs the lead again but his header on 38 minutes went straight at the keeper and he then fired wide of the post when Kaboul's long ball found him in behind a sluggish LA back line after the break.
Spurs should have had a penalty in the 61st minute when Bale was clattered in the box by substitute keeper Brian Rowe - incredibly the referee saw no infringement - and Sigurdsson sidefooted wide from Bale's tee-up soon after when he really should have hit the target.
The game, as with most pre-season friendlies, lost its way following a raft of second-half changes in personnel, although both sides had chances to win it late on.
Aaron Lennon, one of numerous substitutes, had the best opportunity, the England winger's rasping volley deflected just wide of the mark on 83 minutes.
Spurs' tour of the States continues on Saturday when they take on Liverpool in Baltimore before they meet the New York Red Bulls on July 31.