diff --git a/src/memray/commands/run.py b/src/memray/commands/run.py
index 2808ade..e14fb81 100644
--- a/src/memray/commands/run.py
+++ b/src/memray/commands/run.py
@@ -51,18 +51,25 @@ def _run_tracker(
     with tracker:
         pid = os.getpid()
         try:
+            # Determine if we should skip overwriting sys.argv[0]
+            # due to isolated mode (-I) or plain mode (-P) which suppress
+            # the interpreter's automatic path adjustments.
+            skip_argv_overwrite = sys.flags.isolated or getattr(sys.flags, "ignore_environment", False)
             if args.run_as_module:
                 sys.path[0] = os.getcwd()
                 # run_module will replace argv[0] with the script's path
-                sys.argv = ["", *args.script_args]
+                if not skip_argv_overwrite:
+                    sys.argv = ["", *args.script_args]
                 runpy.run_module(args.script, run_name="__main__", alter_sys=True)
             elif args.run_as_cmd:
                 sys.path[0] = ""
-                sys.argv = ["-c", *args.script_args]
+                if not skip_argv_overwrite:
+                    sys.argv = ["-c", *args.script_args]
                 exec(args.script, {"__name__": "__main__"})
             else:
                 sys.path[0] = str(pathlib.Path(args.script).resolve().parent.absolute())
-                sys.argv = [args.script, *args.script_args]
+                if not skip_argv_overwrite:
+                    sys.argv = [args.script, *args.script_args]
                 runpy.run_path(args.script, run_name="__main__")
         finally:
             if not args.quiet and post_run_message is not None and pid == os.getpid():