How to trigger a modal when clicking on a dropdown item in Semantic UI React?

You could use prop open of Modal to programmatically control it. When you detect that the desired Dropdown item was clicked setState appropriately.

Something among those lines.

import * as React from 'react';

export class Demo extends React.Component<{}, {}> {
  state = {
    options: [
      { text: 'doNothing', value: 'doNothing' },
      { text: 'openModal', value: 'openModal' }
    ],
    open: false
  };

  onClose = () => this.setState({open: false});
  onChange = (selected) => {
    // if the correct one is selected then...
    // this.setState({open: true});
  }

  render() {
    return (
      <div>
        <Dropdown
          fluid
          selection
          options={this.options}
          onChange={this.onChange}
          defaultValue={this.options[0].value} />

        <Modal open={this.state.open} onClose={this.onClose}>
          <Modal.Header>Select a Photo</Modal.Header>
          <Modal.Content image>
            <Modal.Description>
              <p>Some contents.</p>
            </Modal.Description>
          </Modal.Content>
        </Modal>
      </div>
    )
  }
}