Yes, it is possible using JOptionPane.showOptionDialog(). Something like this:

JPanel panel = new JPanel();
JLabel label = new JLabel("Enter a password:");
JPasswordField pass = new JPasswordField(10);
panel.add(label);
panel.add(pass);
String[] options = new String[]{"OK", "Cancel"};
int option = JOptionPane.showOptionDialog(null, panel, "The title",
                         JOptionPane.NO_OPTION, JOptionPane.PLAIN_MESSAGE,
                         null, options, options[1]);
if(option == 0) // pressing OK button
{
    char[] password = pass.getPassword();
    System.out.println("Your password is: " + new String(password));
}

The easiest thing is to use JOptionPane's showConfirmDialog method and to pass in a reference to a JPasswordField; e.g.

JPasswordField pf = new JPasswordField();
int okCxl = JOptionPane.showConfirmDialog(null, pf, "Enter Password", JOptionPane.OK_CANCEL_OPTION, JOptionPane.PLAIN_MESSAGE);

if (okCxl == JOptionPane.OK_OPTION) {
  String password = new String(pf.getPassword());
  System.err.println("You entered: " + password);
}

Edit

Below is an example using a custom JPanel to display a message along with the JPasswordField. Per the most recent comment, I've also (hastily) added code to allow the JPasswordField to gain focus when the dialog is first displayed.

public class PasswordPanel extends JPanel {
  private final JPasswordField passwordField = new JPasswordField(12);
  private boolean gainedFocusBefore;

  /**
   * "Hook" method that causes the JPasswordField to request focus the first time this method is called.
   */
  void gainedFocus() {
    if (!gainedFocusBefore) {
      gainedFocusBefore = true;
      passwordField.requestFocusInWindow();
    }
  }

  public PasswordPanel() {
    super(new FlowLayout());

    add(new JLabel("Password: "));
    add(passwordField);
  }

  public char[] getPassword() {
      return passwordField.getPassword();
  }

  public static void main(String[] args) {
      PasswordPanel pPnl = new PasswordPanel();
      JOptionPane op = new JOptionPane(pPnl, JOptionPane.OK_CANCEL_OPTION, JOptionPane.PLAIN_MESSAGE);

      JDialog dlg = op.createDialog("Who Goes There?");

      // Wire up FocusListener to ensure JPasswordField is able to request focus when the dialog is first shown.
      dlg.addWindowFocusListener(new WindowAdapter() {
        @Override
        public void windowGainedFocus(WindowEvent e) {
            pPnl.gainedFocus();
        }
      });

      if (op.getValue() != null && op.getValue().equals(JOptionPane.OK_OPTION)) {
          String password = new String(pPnl.getPassword());
          System.err.println("You entered: " + password);
      }
  }
}