You could see the following post about encryption and decryption
Encrypting & Decrypting a String in C#
Then Encrypt the connectionString value, then before you use the connection string decrypt it
var encrypted = ConfigurationManager.ConnectionStrings["MySqlConnect"].ConnectionString;
var decrypted = StringCipher.Decrypt(encrypted,"yourStrongPassword");
--NEW ANSWER--
The following MSDN Post explains how to encrypt a web.config file, according to them you can just rename your app.config to web.config and then follow the steps to encrypt the web.config file (Just remember to rename it back to app.config)
https://social.msdn.microsoft.com/Forums/windows/en-US/3b5a1d1f-aa57-40d8-8607-fee0b2a8a6db/protect-appconfig-file-or-encrypt.
The alternative route to take is to create your own configuration file using xml/json and then completely Encrypt the xml/json text and store into a file.
public class MyConfiguration
{
public string ConnectionString {get;set;}
}
Now you can create a new instance of MyConfiguration, Serialize it with Json/Xml encrypt the result string and store in a file, copy it to the project where you can read it, decrypt it and deserialize back to an object.
I would first try to use the web.config route and see how that goes