diff --git a/targets/wasm_exec.js b/targets/wasm_exec.js
index fd4c8a04d4..845456aa14 100644
--- a/targets/wasm_exec.js
+++ b/targets/wasm_exec.js
@@ -272,7 +272,11 @@
 					"runtime.sleepTicks": (timeout) => {
 						// Do not sleep, only reactivate the scheduler after the given
 						// timeout, keeping exactly one pending wakeup.
-						const ms = Number(timeout) / 1e6;
+						// Round up to a whole millisecond. Some hosts (Cloudflare
+						// Workers) only advance the clock by a timer's delay rounded
+						// down to a millisecond, so a fractional remainder would be
+						// slept again and again without the clock ever moving.
+						const ms = Math.ceil(Number(timeout) / 1e6);
 						const due = Date.now() + ms;
 						if (this._scheduledWakeup !== undefined) {
 							if (this._scheduledWakeupDue <= due) return;