To answer your question, yes, it is possible to deploy just a Tab - if production has the expected (75%+) code coverage at the time of deployment.
Your situation could arise if 1. developers have created deployed/altered code in production without also adding additional test coverage, or 2. if they have altered test methods so that they no longer cover the code they did at the time they were deployed, since the last deployment.
To remedy this, you will have to speak to your org's developers to bring the code coverage in production to at least 75% - and it's recommended to bring it up higher to avoid situations like this, especially when many people are working within one org. The 75% coverage is a hard limit enforced by Salesforce.