Why do I get a FormatException about semicolons when sending a MailMessage to multiple recipients?

In the code snippet below, I'm getting a FormatException on this.Recipients. More specifically, the message is

An invalid character was found in the mail header: ';'".

Recipients is a string of three email addresses separated by semicolons (;). The list of recipients is read from an app.config file and the data is making it into the Recipients variable successfully.

As far as I know, multiple recipients should be separated by a semicolon. So why am I getting this error, and how can I resolve it?

This is the relevant function:

public bool Send()
{
    MailMessage mailMsg = new MailMessage(this.Sender, this.Recipients, this.Subject, this.Message);

    SmtpClient smtpServer = new SmtpClient(SMTP);
    smtpServer.DeliveryMethod = SmtpDeliveryMethod.Network;
}

This resource says I can use a semicolon as a delimiter.