You ask about the effect on "the supply and demand curve" (I assume you mean curves). Especially when the scenario involves more than one country, it is important to clarify to which good these supply and demand curves relate. Presumably you mean supply of and demand for bananas produced in country A.
A further point to clarify is whether we are concerned with the short term, in which the relevant stocks of capital, in this case banana trees together with any equipment used in harvesting and transport, remain unchanged, or with the long term, in which such capital may vary.
In the short term, a boycott by country B will probably reduce demand, that is, it shifts the whole demand curve to the left. But it should not affect supply, that is, the supply curve as a whole should not shift. Assuming that both supply and demand are moderately elastic, however, the reduction in demand will in turn lower both the equilibrium price and the quantity supplied.
The reason why I include the qualification "probably" in the above is that the effect of the boycott on other countries is unknown. If country B can still obtain bananas of equivalent quality from other banana-exporting countries, and maintains the same total level of banana imports, and if in turn other banana-importing countries maintain their total banana imports, then there would be a possible scenario in which demand for A's bananas remained unchanged, with the reduction in demand from B being exactly offset by increased demand from other countries.
Turning to the long term, how A's banana growers react to the boycott is likely to depend on their experience in the short term. If they find that the price of their bananas falls, and judge that this lower price is likely to be maintained, they will probably respond by reducing the capital they devote to banana growing, including planting other crops on some of the land previously devoted to bananas. In that case the supply of bananas will fall in the long term: more precisely, although the long-run supply curve will not shift, there will be a movement along that curve to the left, to a point on a different short-run supply curve corresponding to the reduced quantity of capital.