.icon {
   background-image: url(./logo.svg);
}

import React, { Component } from 'react'

class Header extends Component {

  render() {
    return (
        <div className='header'>
            <img src={'./logo.svg'} />
        </div>
    );
  }
};

export default Header

import React, { Component } from 'react'
import mySvg from "./logo.svg";

class Header extends Component {

  render() {
    return (
        <div className='header'>
            <div dangerouslySetInnerHTML={{__html: mySvg}} />
        </div>
    );
  }
};

export default Header

import React, { Component } from 'react'

import mySvg from './logo.svg'

class Header extends Component {

  render() {
    return (
        <div className='header'>
            <img src={mySvg} />
        </div>
    );
  }
};

export default Header

{
      test: /.svg$/,
      loader: 'raw-loader'
 }

import closeIcon from 'svg/ic_close_black_24px.svg';

<button id="closeModal">
  {{{closeIcon}}}
</button>

<button id="closeModal">
  <svg fill="#000000" height="24" viewBox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg">
    <path d="M19 6.41L17.59 5 12 10.59 6.41 5 5 6.41 10.59 12 5 17.59 6.41 19 12 13.41 17.59 19 19 17.59 13.41 12z"></path>
    <path d="M0 0h24v24H0z" fill="none"></path>
  </svg>
</button>