Предпосылка

* babel-jest
* @babel/preset-env
* @babel/plugin-proposal-class-properties


npm install jest babel-jest @babel/preset-env @babel/plugin-proposal-class-properties

babel.config.json

{
    "presets": ["@babel/preset-env"],
    "plugins": ["@babel/plugin-proposal-class-properties"]
}

package.json

{
  "name": "jest-hello-world",
  "version": "1.0.0",
  "description": "",
  "main": "index.js",
  "scripts": {
    "test": "jest"
  },
  "author": "",
  "license": "ISC",
  "dependencies": {
    "@babel/plugin-proposal-class-properties": "^7.10.4",
    "@babel/preset-env": "^7.10.4",
    "babel-jest": "^26.1.0",
    "jest": "^26.1.0"
  }
}

источник/hello.js

export class Hello {
    name;

    returnName() {
        return this.name;
    }
}

источник/hello.test.js

import {Hello} from "./hello";

test('test returnName if the result is as same as name', ()=>{
    const hello = new Hello();
    hello.name = "testing";
    expect(hello.returnName()).toBe("testing");
})

Выполнить

npm run test

Результат

```
 PASS  src/hello.test.js
  √ test returnName if the result is as same as name (1 ms)

Test Suites: 1 passed, 1 total
Tests:       1 passed, 1 total
Snapshots:   0 total
Time:        5.564 s, estimated 11 s
Ran all test suites.
```