testComponent.js

import icon from './assets/icon.svg';

class myComponent extends React.Component {
  render() {
    return (
      <UnrelatedWrapper>
        <SVGWrapper dangerouslySetInnerHTML={{__html: icon}} />
      </UnrelatedWrapper>
    );
  }
}

const SVGWrapper = styled.span`
  background-color: red;

  svg {
    background-color: blue;
  }
`