Members of the Public and Commercial Services union (PCS) and Prospect union walked out of the central London attraction at 1230 BST.
Staff have rejected a 1.6% pay rise, plus a £100 bonus, and plan an indefinite work to rule from next week.
Managers said the museum would remain open during the strike although access to some galleries may be restricted.
PCS general secretary Mark Serwotka said: "This action is a direct result of the government's shameful policy of attacking the living standards of public sector workers by capping pay rises to 2%."
Union members are angry that the pay rise has been imposed despite being rejected by union members.
Staff at The National Gallery in Trafalgar Square also walked out on Friday as part of the dispute.
BBC
| Buying | Selling | |
| Euro | 1.7314 | 1.7398 |
| Dolar | 1.1746 | 1.1803 |
| Sterlin | 2.1482 | 2.1594 |













