diff --git a/drake/multibody/dev/BUILD b/drake/multibody/dev/BUILD
index 0c585d748ccc..d6ab215705d6 100644
--- a/drake/multibody/dev/BUILD
+++ b/drake/multibody/dev/BUILD
@@ -35,7 +35,8 @@ drake_cc_googletest(
     data = [
         "//drake/manipulation/models/iiwa_description:models",
     ],
-    tags = gurobi_test_tags(),
+    # Excluding because an assertion fails in LLVM code. Issue #6179.
+    tags = gurobi_test_tags() + ["no_tsan"],
     deps = [
         ":global_inverse_kinematics_test_util",
     ],
@@ -48,7 +49,8 @@ drake_cc_googletest(
     data = [
         "//drake/manipulation/models/iiwa_description:models",
     ],
-    tags = gurobi_test_tags(),
+    # Excluding because an assertion fails in LLVM code. Issue #6179.
+    tags = gurobi_test_tags() + ["no_tsan"],
     deps = [
         ":global_inverse_kinematics_test_util",
     ],
@@ -61,7 +63,8 @@ drake_cc_googletest(
     data = [
         "//drake/manipulation/models/iiwa_description:models",
     ],
-    tags = gurobi_test_tags(),
+    # Excluding because an assertion fails in LLVM code. Issue #6179.
+    tags = gurobi_test_tags() + ["no_tsan"],
     deps = [
         ":global_inverse_kinematics_test_util",
     ],
diff --git a/drake/solvers/BUILD b/drake/solvers/BUILD
index b949504d9b24..9d335c043d2c 100644
--- a/drake/solvers/BUILD
+++ b/drake/solvers/BUILD
@@ -648,7 +648,8 @@ drake_cc_googletest(
 drake_cc_googletest(
     name = "rotation_constraint_test",
     size = "medium",
-    tags = gurobi_test_tags() + mosek_test_tags(),
+    # Excluding because an assertion fails in LLVM code. Issue #6179.
+    tags = gurobi_test_tags() + mosek_test_tags() + ["no_tsan"],
     deps = [
         ":gurobi_solver",
         ":mathematical_program",
@@ -672,7 +673,8 @@ drake_cc_binary(
 drake_cc_googletest(
     name = "rotation_constraint_limit_test",
     size = "large",
-    tags = gurobi_test_tags(),
+    # Excluding because an assertion fails in LLVM code. Issue #6179.
+    tags = gurobi_test_tags() + ["no_tsan"],
     deps = [
         ":gurobi_solver",
         ":mathematical_program",
diff --git a/tools/tsan.supp b/tools/tsan.supp
index 109e4203a0cc..c0ac1956ff5e 100644
--- a/tools/tsan.supp
+++ b/tools/tsan.supp
@@ -20,5 +20,8 @@ race:__kmp_launch_monitor
 # thread leak (libiomp5.*) in __kmp_create_worker
 thread:__kmp_create_worker
 
+# thread leak (libiomp5.*) in __kmp_create_monitor
+thread:__kmp_create_monitor
+
 # data race (libglib-2.0.*) in g_static_rec_mutex_lock
 race:g_static_rec_mutex_lock