diff --git a/packages/cli/.changesets/remove-dependency-on---appsignal-core-.md b/packages/cli/.changesets/remove-dependency-on---appsignal-core-.md
new file mode 100644
index 00000000..8ed954ca
--- /dev/null
+++ b/packages/cli/.changesets/remove-dependency-on---appsignal-core-.md
@@ -0,0 +1,6 @@
+---
+bump: "patch"
+type: "remove"
+---
+
+Remove dependency on `@appsignal/core`.
diff --git a/packages/cli/package.json b/packages/cli/package.json
index 91f6eb31..d2970881 100644
--- a/packages/cli/package.json
+++ b/packages/cli/package.json
@@ -20,7 +20,7 @@
     "access": "public"
   },
   "dependencies": {
-    "@appsignal/core": "=1.1.21",
+    "isomorphic-unfetch": "=4.0.0",
     "chalk": "^4.1.0",
     "commander": "^6.2.1",
     "inquirer": "^7.3.3"
diff --git a/packages/cli/src/installers/node/index.ts b/packages/cli/src/installers/node/index.ts
index 85294f23..036933fa 100644
--- a/packages/cli/src/installers/node/index.ts
+++ b/packages/cli/src/installers/node/index.ts
@@ -2,7 +2,7 @@ import { existsSync } from "fs"
 import { spawnSync } from "child_process"
 import chalk from "chalk"
 import inquirer from "inquirer"
-import { validatePushApiKey } from "@appsignal/core"
+import { validatePushApiKey } from "../../utils"
 import * as fs from "fs"
 import * as path from "path"
 
diff --git a/packages/cli/src/utils.ts b/packages/cli/src/utils.ts
index 85cbc9a4..bfd5812b 100644
--- a/packages/cli/src/utils.ts
+++ b/packages/cli/src/utils.ts
@@ -1,5 +1,6 @@
 import { existsSync } from "fs"
 import { dirname } from "path"
+import fetch from "isomorphic-unfetch"
 
 // Returns the filesystem location at which the root of the
 // `@appsignal/nodejs` package was found.
@@ -46,3 +47,24 @@ export function checkForAppsignalPackage(): string {
 
   process.exit(1)
 }
+
+export async function validatePushApiKey({
+  endpoint = "https://push.appsignal.com",
+  apiKey
+}: {
+  endpoint?: string
+  apiKey: string
+}) {
+  const { status } = await fetch(`${endpoint}/1/auth?api_key=${apiKey}`)
+
+  switch (status) {
+    case 200:
+      return true
+    case 401:
+      return false
+    default:
+      throw new Error(
+        `Invalid ${status} response from server when authenticating`
+      )
+  }
+}
diff --git a/packages/core/.changesets/remove-dependency-on--isomorphic-unfetch-.md b/packages/core/.changesets/remove-dependency-on--isomorphic-unfetch-.md
new file mode 100644
index 00000000..8c58d8c1
--- /dev/null
+++ b/packages/core/.changesets/remove-dependency-on--isomorphic-unfetch-.md
@@ -0,0 +1,7 @@
+---
+bump: "patch"
+type: "remove"
+---
+
+Remove dependency on `isomorphic-unfetch`. This fixes an issue where
+`isomorphic-unfetch` fails to bundle properly with `esbuild` or `webpack`.
diff --git a/packages/core/package.json b/packages/core/package.json
index 4c9b4232..970a7b7a 100644
--- a/packages/core/package.json
+++ b/packages/core/package.json
@@ -26,7 +26,6 @@
   },
   "dependencies": {
     "@appsignal/types": "=3.0.1",
-    "isomorphic-unfetch": "^4.0.0",
     "tslib": "^2.3.0"
   }
 }
diff --git a/packages/core/src/index.ts b/packages/core/src/index.ts
index 50d53781..83087b4e 100644
--- a/packages/core/src/index.ts
+++ b/packages/core/src/index.ts
@@ -5,7 +5,6 @@ export * from "./utils/error"
 export * from "./utils/url"
 export * from "./utils/async"
 export * from "./utils/environment"
-export * from "./utils/push-api"
 
 // Classes
 export { Serializable } from "./serializable"
diff --git a/packages/core/src/utils/push-api.ts b/packages/core/src/utils/push-api.ts
deleted file mode 100644
index aab51f8e..00000000
--- a/packages/core/src/utils/push-api.ts
+++ /dev/null
@@ -1,22 +0,0 @@
-import fetch from "isomorphic-unfetch"
-
-export async function validatePushApiKey({
-  endpoint = "https://push.appsignal.com",
-  apiKey
-}: {
-  endpoint?: string
-  apiKey: string
-}) {
-  const { status } = await fetch(`${endpoint}/1/auth?api_key=${apiKey}`)
-
-  switch (status) {
-    case 200:
-      return true
-    case 401:
-      return false
-    default:
-      throw new Error(
-        `Invalid ${status} response from server when authenticating`
-      )
-  }
-}