PhpMyAdmin would probably work for this.
http://www.phpmyadmin.net/home_page/index.php

Lots of hosts have it pre-installed.

Excel can import CSV files, and most databases can dump data as CSV. You could potentially use something like Sequel Pro locally to do this.

Honestly, without knowing the WHY behind the need, it's tough to say what the right solution is.

Really, manually syncing an Excel document back and forth with a database seems like a complex and fragile solution to a problem. Is it possible you could remove the Excel sheet from the equation? Or use Google Sheets to make it available collaboratively online?

Depending on the problem you're trying to solve, there's probably a much easier solution that a SQL import/export.

I'd be happy to go over solutions and help you find a simpler way to solve this problem if you'd like. Just tag me for a quick call.

Good luck!

You can hire a freelancer (e.g. from freelancer.com) to write a simple web program to do that. Shouldn't take more than a couple hours.

Lot of missing info in this question.

Like, how data will be accessed (frequency).

This will determine your SQL storage engine type + table structure.

You can also adjust your table structure to protect against duplicate entries.

This is important, if it takes a long time to load your data. If you setup your structure to only allow unique data, then you can just upload your new data, without having to "drop" (destroy) your old data.

This can potentially speed up your data loads considerably, especially if you're using cheap/slow hosting for your database.

Likely good to give equal consideration to how data is used first + data loading.